added tests for other elements

diff --git a/tests/fe/fe_dgp_3rd_derivative_divergence_theorem.cc b/tests/fe/fe_dgp_3rd_derivative_divergence_theorem.cc
new file mode 100644 (file)
index 0000000..0e0c35a
--- /dev/null
+++ b/tests/fe/fe_dgp_3rd_derivative_divergence_theorem.cc
@@ -0,0 +1,177 @@
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2003 - 2015 by the deal.II authors
+//
+// This file is part of the deal.II library.
+//
+// The deal.II library is free software; you can use it, redistribute
+// it, and/or modify it under the terms of the GNU Lesser General
+// Public License as published by the Free Software Foundation; either
+// version 2.1 of the License, or (at your option) any later version.
+// The full text of the license can be found in the file LICENSE at
+// the top level of the deal.II distribution.
+//
+// ---------------------------------------------------------------------
+
+
+// check the correctness of fe_values.shape_3rd_derivative for FE_DGP by comparing
+// the integral of all shape third derivative components with the flux of the
+// hessian over the boundary by the divergence theorem
+
+#include "../tests.h"
+#include <deal.II/base/logstream.h>
+#include <deal.II/base/function.h>
+#include <deal.II/base/quadrature_lib.h>
+#include <deal.II/lac/vector.h>
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/tria_boundary_lib.h>
+#include <deal.II/dofs/dof_handler.h>
+#include <deal.II/fe/fe_q.h>
+#include <deal.II/fe/fe_dgp.h>
+#include <deal.II/fe/fe_raviart_thomas.h>
+#include <deal.II/fe/fe_nedelec.h>
+#include <deal.II/fe/fe_dgq.h>
+#include <deal.II/fe/fe_system.h>
+#include <deal.II/fe/fe_values.h>
+#include <deal.II/fe/mapping_q1.h>
+
+#include <sstream>
+#include <fstream>
+
+template<int dim>
+Tensor<1,dim> ones ()
+{
+  Tensor<1,dim> result;
+  for (unsigned int i=0; i<dim; ++i)
+    result[i] = 1.0;
+  return result;
+}
+
+template<int dim>
+void test (const Triangulation<dim> &tr,
+           const FiniteElement<dim> &fe,
+           const double tolerance)
+{
+  DoFHandler<dim> dof(tr);
+  dof.distribute_dofs(fe);
+
+  std::stringstream ss;
+
+  deallog << "FE=" << fe.get_name() << std::endl;
+
+  const QGauss<dim> quadrature(6);
+  FEValues<dim> fe_values (fe, quadrature, update_3rd_derivatives
+                           | update_quadrature_points
+                           | update_JxW_values);
+
+  const QGauss<dim-1> face_quadrature(6);
+  FEFaceValues<dim> fe_face_values (fe, face_quadrature,
+                                    update_hessians
+                                    | update_quadrature_points
+                                    | update_normal_vectors
+                                    | update_JxW_values);
+
+  for (typename DoFHandler<dim>::active_cell_iterator cell = dof.begin_active();
+       cell != dof.end();
+       ++cell)
+    {
+      fe_values.reinit (cell);
+
+      deallog << "Cell nodes:" << std::endl;
+      for (unsigned int i=0; i<GeometryInfo<dim>::vertices_per_cell; ++i)
+        {
+          deallog << i << ": ( ";
+          for (unsigned int d=0; d<dim; ++d)
+            deallog << cell->vertex(i)[d] << " ";
+          deallog << ")" << std::endl;
+        }
+
+      bool cell_ok = true;
+
+      for (unsigned int c=0; c<fe.n_components(); ++c)
+        {
+          FEValuesExtractors::Scalar single_component (c);
+
+          for (unsigned int i=0; i<fe_values.dofs_per_cell; ++i)
+            {
+              ss << "component=" << c
+                 << ", dof=" << i
+                 << std::endl;
+
+              Tensor<3,dim> bulk_integral;
+              for (unsigned int q=0; q<fe_values.n_quadrature_points; ++q)
+                {
+                  bulk_integral += fe_values[single_component].third_derivative(i,q) * fe_values.JxW(q);
+
+                  Tensor<3,dim> third_derivative = fe_values[single_component].third_derivative(i,q);
+                }
+
+              Tensor<3,dim> boundary_integral;
+              for (unsigned int face=0; face<GeometryInfo<dim>::faces_per_cell; ++face)
+                {
+                  fe_face_values.reinit(cell,face);
+                  for (unsigned int q=0; q<fe_face_values.n_quadrature_points; ++q)
+                    {
+                      Tensor<2,dim> hessian = fe_face_values[single_component].hessian (i,q);
+                      Tensor<3,dim> hessian_normal_outer_prod;
+
+                      outer_product(hessian_normal_outer_prod, hessian, fe_face_values.normal_vector(q));
+                      boundary_integral += hessian_normal_outer_prod * fe_face_values.JxW(q);
+                    }
+                }
+
+              if ((bulk_integral-boundary_integral).norm_square() > tolerance * (bulk_integral.norm() + boundary_integral.norm()))
+                {
+                  deallog << "Failed:" << std::endl;
+                  deallog << ss.str() << std::endl;
+                  deallog << "    bulk integral=" << bulk_integral << std::endl;
+                  deallog << "boundary integral=" << boundary_integral << std::endl;
+                  deallog << "Error! difference between bulk and surface integrals is "
+                          << (bulk_integral-boundary_integral).norm_square()
+                          << " and greater than "
+                          << tolerance * (bulk_integral.norm() + boundary_integral.norm())
+                          << "!\n\n" << std::endl;
+                  cell_ok = false;
+                }
+
+              ss.str("");
+            }
+        }
+
+      deallog << (cell_ok? "OK: cell bulk and boundary integrals match...\n" : "Failed divergence test...\n") << std::endl;
+    }
+}
+
+
+
+template<int dim>
+void test_hyper_ball(const double tolerance)
+{
+  Triangulation<dim> tr;
+  GridGenerator::hyper_ball(tr);
+
+  static const HyperBallBoundary<dim> boundary;
+  tr.set_boundary (0, boundary);
+
+  tr.refine_global(1);
+
+  FE_DGP<dim>  fe(2);
+  test(tr, fe, tolerance);
+}
+
+
+int main()
+{
+  std::ofstream logfile ("output");
+  deallog << std::setprecision (3);
+
+  deallog.attach(logfile);
+  deallog.depth_console (0);
+  deallog.threshold_double(1.e-7);
+
+  test_hyper_ball<2>(1e-6);
+  test_hyper_ball<3>(1e-6);
+
+  deallog << "done..." << std::endl;
+}
+

diff --git a/tests/fe/fe_dgp_3rd_derivative_divergence_theorem.output b/tests/fe/fe_dgp_3rd_derivative_divergence_theorem.output
new file mode 100644 (file)
index 0000000..e758ca4
--- /dev/null
+++ b/tests/fe/fe_dgp_3rd_derivative_divergence_theorem.output
@@ -0,0 +1,760 @@
+
+DEAL::FE=FE_DGP<2>(2)
+DEAL::Cell nodes:
+DEAL::0: ( -0.707 -0.707 )
+DEAL::1: ( 0 -1.00 )
+DEAL::2: ( -0.500 -0.500 )
+DEAL::3: ( 0 -0.646 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 -1.00 )
+DEAL::1: ( 0.707 -0.707 )
+DEAL::2: ( 0 -0.646 )
+DEAL::3: ( 0.500 -0.500 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.500 -0.500 )
+DEAL::1: ( 0 -0.646 )
+DEAL::2: ( -0.293 -0.293 )
+DEAL::3: ( 0 -0.293 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 -0.646 )
+DEAL::1: ( 0.500 -0.500 )
+DEAL::2: ( 0 -0.293 )
+DEAL::3: ( 0.293 -0.293 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.707 -0.707 )
+DEAL::1: ( -0.500 -0.500 )
+DEAL::2: ( -1.00 0 )
+DEAL::3: ( -0.646 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.500 -0.500 )
+DEAL::1: ( -0.293 -0.293 )
+DEAL::2: ( -0.646 0 )
+DEAL::3: ( -0.293 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -1.00 0 )
+DEAL::1: ( -0.646 0 )
+DEAL::2: ( -0.707 0.707 )
+DEAL::3: ( -0.500 0.500 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.646 0 )
+DEAL::1: ( -0.293 0 )
+DEAL::2: ( -0.500 0.500 )
+DEAL::3: ( -0.293 0.293 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.293 -0.293 )
+DEAL::1: ( 0 -0.293 )
+DEAL::2: ( -0.293 0 )
+DEAL::3: ( 0 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 -0.293 )
+DEAL::1: ( 0.293 -0.293 )
+DEAL::2: ( 0 0 )
+DEAL::3: ( 0.293 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.293 0 )
+DEAL::1: ( 0 0 )
+DEAL::2: ( -0.293 0.293 )
+DEAL::3: ( 0 0.293 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 0 )
+DEAL::1: ( 0.293 0 )
+DEAL::2: ( 0 0.293 )
+DEAL::3: ( 0.293 0.293 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.707 -0.707 )
+DEAL::1: ( 1.00 0 )
+DEAL::2: ( 0.500 -0.500 )
+DEAL::3: ( 0.646 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 1.00 0 )
+DEAL::1: ( 0.707 0.707 )
+DEAL::2: ( 0.646 0 )
+DEAL::3: ( 0.500 0.500 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.500 -0.500 )
+DEAL::1: ( 0.646 0 )
+DEAL::2: ( 0.293 -0.293 )
+DEAL::3: ( 0.293 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.646 0 )
+DEAL::1: ( 0.500 0.500 )
+DEAL::2: ( 0.293 0 )
+DEAL::3: ( 0.293 0.293 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.707 0.707 )
+DEAL::1: ( -0.500 0.500 )
+DEAL::2: ( 0 1.00 )
+DEAL::3: ( 0 0.646 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.500 0.500 )
+DEAL::1: ( -0.293 0.293 )
+DEAL::2: ( 0 0.646 )
+DEAL::3: ( 0 0.293 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 1.00 )
+DEAL::1: ( 0 0.646 )
+DEAL::2: ( 0.707 0.707 )
+DEAL::3: ( 0.500 0.500 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 0.646 )
+DEAL::1: ( 0 0.293 )
+DEAL::2: ( 0.500 0.500 )
+DEAL::3: ( 0.293 0.293 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::FE=FE_DGP<3>(2)
+DEAL::Cell nodes:
+DEAL::0: ( -0.211 -0.211 -0.211 )
+DEAL::1: ( 0 -0.211 -0.211 )
+DEAL::2: ( -0.211 0 -0.211 )
+DEAL::3: ( 0 0 -0.211 )
+DEAL::4: ( -0.211 -0.211 0 )
+DEAL::5: ( 0 -0.211 0 )
+DEAL::6: ( -0.211 0 0 )
+DEAL::7: ( 0 0 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 -0.211 -0.211 )
+DEAL::1: ( 0.211 -0.211 -0.211 )
+DEAL::2: ( 0 0 -0.211 )
+DEAL::3: ( 0.211 0 -0.211 )
+DEAL::4: ( 0 -0.211 0 )
+DEAL::5: ( 0.211 -0.211 0 )
+DEAL::6: ( 0 0 0 )
+DEAL::7: ( 0.211 0 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.211 0 -0.211 )
+DEAL::1: ( 0 0 -0.211 )
+DEAL::2: ( -0.211 0.211 -0.211 )
+DEAL::3: ( 0 0.211 -0.211 )
+DEAL::4: ( -0.211 0 0 )
+DEAL::5: ( 0 0 0 )
+DEAL::6: ( -0.211 0.211 0 )
+DEAL::7: ( 0 0.211 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 0 -0.211 )
+DEAL::1: ( 0.211 0 -0.211 )
+DEAL::2: ( 0 0.211 -0.211 )
+DEAL::3: ( 0.211 0.211 -0.211 )
+DEAL::4: ( 0 0 0 )
+DEAL::5: ( 0.211 0 0 )
+DEAL::6: ( 0 0.211 0 )
+DEAL::7: ( 0.211 0.211 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.211 -0.211 0 )
+DEAL::1: ( 0 -0.211 0 )
+DEAL::2: ( -0.211 0 0 )
+DEAL::3: ( 0 0 0 )
+DEAL::4: ( -0.211 -0.211 0.211 )
+DEAL::5: ( 0 -0.211 0.211 )
+DEAL::6: ( -0.211 0 0.211 )
+DEAL::7: ( 0 0 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 -0.211 0 )
+DEAL::1: ( 0.211 -0.211 0 )
+DEAL::2: ( 0 0 0 )
+DEAL::3: ( 0.211 0 0 )
+DEAL::4: ( 0 -0.211 0.211 )
+DEAL::5: ( 0.211 -0.211 0.211 )
+DEAL::6: ( 0 0 0.211 )
+DEAL::7: ( 0.211 0 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.211 0 0 )
+DEAL::1: ( 0 0 0 )
+DEAL::2: ( -0.211 0.211 0 )
+DEAL::3: ( 0 0.211 0 )
+DEAL::4: ( -0.211 0 0.211 )
+DEAL::5: ( 0 0 0.211 )
+DEAL::6: ( -0.211 0.211 0.211 )
+DEAL::7: ( 0 0.211 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 0 0 )
+DEAL::1: ( 0.211 0 0 )
+DEAL::2: ( 0 0.211 0 )
+DEAL::3: ( 0.211 0.211 0 )
+DEAL::4: ( 0 0 0.211 )
+DEAL::5: ( 0.211 0 0.211 )
+DEAL::6: ( 0 0.211 0.211 )
+DEAL::7: ( 0.211 0.211 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.577 -0.577 -0.577 )
+DEAL::1: ( 0 -0.707 -0.707 )
+DEAL::2: ( -0.707 0 -0.707 )
+DEAL::3: ( 0 0 -1.00 )
+DEAL::4: ( -0.394 -0.394 -0.394 )
+DEAL::5: ( 0 -0.419 -0.419 )
+DEAL::6: ( -0.419 0 -0.419 )
+DEAL::7: ( 0 0 -0.457 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 -0.707 -0.707 )
+DEAL::1: ( 0.577 -0.577 -0.577 )
+DEAL::2: ( 0 0 -1.00 )
+DEAL::3: ( 0.707 0 -0.707 )
+DEAL::4: ( 0 -0.419 -0.419 )
+DEAL::5: ( 0.394 -0.394 -0.394 )
+DEAL::6: ( 0 0 -0.457 )
+DEAL::7: ( 0.419 0 -0.419 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.707 0 -0.707 )
+DEAL::1: ( 0 0 -1.00 )
+DEAL::2: ( -0.577 0.577 -0.577 )
+DEAL::3: ( 0 0.707 -0.707 )
+DEAL::4: ( -0.419 0 -0.419 )
+DEAL::5: ( 0 0 -0.457 )
+DEAL::6: ( -0.394 0.394 -0.394 )
+DEAL::7: ( 0 0.419 -0.419 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 0 -1.00 )
+DEAL::1: ( 0.707 0 -0.707 )
+DEAL::2: ( 0 0.707 -0.707 )
+DEAL::3: ( 0.577 0.577 -0.577 )
+DEAL::4: ( 0 0 -0.457 )
+DEAL::5: ( 0.419 0 -0.419 )
+DEAL::6: ( 0 0.419 -0.419 )
+DEAL::7: ( 0.394 0.394 -0.394 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.394 -0.394 -0.394 )
+DEAL::1: ( 0 -0.419 -0.419 )
+DEAL::2: ( -0.419 0 -0.419 )
+DEAL::3: ( 0 0 -0.457 )
+DEAL::4: ( -0.211 -0.211 -0.211 )
+DEAL::5: ( 0 -0.211 -0.211 )
+DEAL::6: ( -0.211 0 -0.211 )
+DEAL::7: ( 0 0 -0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 -0.419 -0.419 )
+DEAL::1: ( 0.394 -0.394 -0.394 )
+DEAL::2: ( 0 0 -0.457 )
+DEAL::3: ( 0.419 0 -0.419 )
+DEAL::4: ( 0 -0.211 -0.211 )
+DEAL::5: ( 0.211 -0.211 -0.211 )
+DEAL::6: ( 0 0 -0.211 )
+DEAL::7: ( 0.211 0 -0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.419 0 -0.419 )
+DEAL::1: ( 0 0 -0.457 )
+DEAL::2: ( -0.394 0.394 -0.394 )
+DEAL::3: ( 0 0.419 -0.419 )
+DEAL::4: ( -0.211 0 -0.211 )
+DEAL::5: ( 0 0 -0.211 )
+DEAL::6: ( -0.211 0.211 -0.211 )
+DEAL::7: ( 0 0.211 -0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 0 -0.457 )
+DEAL::1: ( 0.419 0 -0.419 )
+DEAL::2: ( 0 0.419 -0.419 )
+DEAL::3: ( 0.394 0.394 -0.394 )
+DEAL::4: ( 0 0 -0.211 )
+DEAL::5: ( 0.211 0 -0.211 )
+DEAL::6: ( 0 0.211 -0.211 )
+DEAL::7: ( 0.211 0.211 -0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.577 -0.577 -0.577 )
+DEAL::1: ( 0.707 0 -0.707 )
+DEAL::2: ( 0.394 -0.394 -0.394 )
+DEAL::3: ( 0.419 0 -0.419 )
+DEAL::4: ( 0.707 -0.707 0 )
+DEAL::5: ( 1.00 0 0 )
+DEAL::6: ( 0.419 -0.419 0 )
+DEAL::7: ( 0.457 0 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.707 0 -0.707 )
+DEAL::1: ( 0.577 0.577 -0.577 )
+DEAL::2: ( 0.419 0 -0.419 )
+DEAL::3: ( 0.394 0.394 -0.394 )
+DEAL::4: ( 1.00 0 0 )
+DEAL::5: ( 0.707 0.707 0 )
+DEAL::6: ( 0.457 0 0 )
+DEAL::7: ( 0.419 0.419 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.394 -0.394 -0.394 )
+DEAL::1: ( 0.419 0 -0.419 )
+DEAL::2: ( 0.211 -0.211 -0.211 )
+DEAL::3: ( 0.211 0 -0.211 )
+DEAL::4: ( 0.419 -0.419 0 )
+DEAL::5: ( 0.457 0 0 )
+DEAL::6: ( 0.211 -0.211 0 )
+DEAL::7: ( 0.211 0 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.419 0 -0.419 )
+DEAL::1: ( 0.394 0.394 -0.394 )
+DEAL::2: ( 0.211 0 -0.211 )
+DEAL::3: ( 0.211 0.211 -0.211 )
+DEAL::4: ( 0.457 0 0 )
+DEAL::5: ( 0.419 0.419 0 )
+DEAL::6: ( 0.211 0 0 )
+DEAL::7: ( 0.211 0.211 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.707 -0.707 0 )
+DEAL::1: ( 1.00 0 0 )
+DEAL::2: ( 0.419 -0.419 0 )
+DEAL::3: ( 0.457 0 0 )
+DEAL::4: ( 0.577 -0.577 0.577 )
+DEAL::5: ( 0.707 0 0.707 )
+DEAL::6: ( 0.394 -0.394 0.394 )
+DEAL::7: ( 0.419 0 0.419 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 1.00 0 0 )
+DEAL::1: ( 0.707 0.707 0 )
+DEAL::2: ( 0.457 0 0 )
+DEAL::3: ( 0.419 0.419 0 )
+DEAL::4: ( 0.707 0 0.707 )
+DEAL::5: ( 0.577 0.577 0.577 )
+DEAL::6: ( 0.419 0 0.419 )
+DEAL::7: ( 0.394 0.394 0.394 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.419 -0.419 0 )
+DEAL::1: ( 0.457 0 0 )
+DEAL::2: ( 0.211 -0.211 0 )
+DEAL::3: ( 0.211 0 0 )
+DEAL::4: ( 0.394 -0.394 0.394 )
+DEAL::5: ( 0.419 0 0.419 )
+DEAL::6: ( 0.211 -0.211 0.211 )
+DEAL::7: ( 0.211 0 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.457 0 0 )
+DEAL::1: ( 0.419 0.419 0 )
+DEAL::2: ( 0.211 0 0 )
+DEAL::3: ( 0.211 0.211 0 )
+DEAL::4: ( 0.419 0 0.419 )
+DEAL::5: ( 0.394 0.394 0.394 )
+DEAL::6: ( 0.211 0 0.211 )
+DEAL::7: ( 0.211 0.211 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.577 -0.577 0.577 )
+DEAL::1: ( 0 -0.707 0.707 )
+DEAL::2: ( -0.394 -0.394 0.394 )
+DEAL::3: ( 0 -0.419 0.419 )
+DEAL::4: ( -0.707 0 0.707 )
+DEAL::5: ( 0 0 1.00 )
+DEAL::6: ( -0.419 0 0.419 )
+DEAL::7: ( 0 0 0.457 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 -0.707 0.707 )
+DEAL::1: ( 0.577 -0.577 0.577 )
+DEAL::2: ( 0 -0.419 0.419 )
+DEAL::3: ( 0.394 -0.394 0.394 )
+DEAL::4: ( 0 0 1.00 )
+DEAL::5: ( 0.707 0 0.707 )
+DEAL::6: ( 0 0 0.457 )
+DEAL::7: ( 0.419 0 0.419 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.394 -0.394 0.394 )
+DEAL::1: ( 0 -0.419 0.419 )
+DEAL::2: ( -0.211 -0.211 0.211 )
+DEAL::3: ( 0 -0.211 0.211 )
+DEAL::4: ( -0.419 0 0.419 )
+DEAL::5: ( 0 0 0.457 )
+DEAL::6: ( -0.211 0 0.211 )
+DEAL::7: ( 0 0 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 -0.419 0.419 )
+DEAL::1: ( 0.394 -0.394 0.394 )
+DEAL::2: ( 0 -0.211 0.211 )
+DEAL::3: ( 0.211 -0.211 0.211 )
+DEAL::4: ( 0 0 0.457 )
+DEAL::5: ( 0.419 0 0.419 )
+DEAL::6: ( 0 0 0.211 )
+DEAL::7: ( 0.211 0 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.707 0 0.707 )
+DEAL::1: ( 0 0 1.00 )
+DEAL::2: ( -0.419 0 0.419 )
+DEAL::3: ( 0 0 0.457 )
+DEAL::4: ( -0.577 0.577 0.577 )
+DEAL::5: ( 0 0.707 0.707 )
+DEAL::6: ( -0.394 0.394 0.394 )
+DEAL::7: ( 0 0.419 0.419 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 0 1.00 )
+DEAL::1: ( 0.707 0 0.707 )
+DEAL::2: ( 0 0 0.457 )
+DEAL::3: ( 0.419 0 0.419 )
+DEAL::4: ( 0 0.707 0.707 )
+DEAL::5: ( 0.577 0.577 0.577 )
+DEAL::6: ( 0 0.419 0.419 )
+DEAL::7: ( 0.394 0.394 0.394 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.419 0 0.419 )
+DEAL::1: ( 0 0 0.457 )
+DEAL::2: ( -0.211 0 0.211 )
+DEAL::3: ( 0 0 0.211 )
+DEAL::4: ( -0.394 0.394 0.394 )
+DEAL::5: ( 0 0.419 0.419 )
+DEAL::6: ( -0.211 0.211 0.211 )
+DEAL::7: ( 0 0.211 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 0 0.457 )
+DEAL::1: ( 0.419 0 0.419 )
+DEAL::2: ( 0 0 0.211 )
+DEAL::3: ( 0.211 0 0.211 )
+DEAL::4: ( 0 0.419 0.419 )
+DEAL::5: ( 0.394 0.394 0.394 )
+DEAL::6: ( 0 0.211 0.211 )
+DEAL::7: ( 0.211 0.211 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.577 -0.577 -0.577 )
+DEAL::1: ( -0.394 -0.394 -0.394 )
+DEAL::2: ( -0.707 0 -0.707 )
+DEAL::3: ( -0.419 0 -0.419 )
+DEAL::4: ( -0.707 -0.707 0 )
+DEAL::5: ( -0.419 -0.419 0 )
+DEAL::6: ( -1.00 0 0 )
+DEAL::7: ( -0.457 0 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.394 -0.394 -0.394 )
+DEAL::1: ( -0.211 -0.211 -0.211 )
+DEAL::2: ( -0.419 0 -0.419 )
+DEAL::3: ( -0.211 0 -0.211 )
+DEAL::4: ( -0.419 -0.419 0 )
+DEAL::5: ( -0.211 -0.211 0 )
+DEAL::6: ( -0.457 0 0 )
+DEAL::7: ( -0.211 0 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.707 0 -0.707 )
+DEAL::1: ( -0.419 0 -0.419 )
+DEAL::2: ( -0.577 0.577 -0.577 )
+DEAL::3: ( -0.394 0.394 -0.394 )
+DEAL::4: ( -1.00 0 0 )
+DEAL::5: ( -0.457 0 0 )
+DEAL::6: ( -0.707 0.707 0 )
+DEAL::7: ( -0.419 0.419 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.419 0 -0.419 )
+DEAL::1: ( -0.211 0 -0.211 )
+DEAL::2: ( -0.394 0.394 -0.394 )
+DEAL::3: ( -0.211 0.211 -0.211 )
+DEAL::4: ( -0.457 0 0 )
+DEAL::5: ( -0.211 0 0 )
+DEAL::6: ( -0.419 0.419 0 )
+DEAL::7: ( -0.211 0.211 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.707 -0.707 0 )
+DEAL::1: ( -0.419 -0.419 0 )
+DEAL::2: ( -1.00 0 0 )
+DEAL::3: ( -0.457 0 0 )
+DEAL::4: ( -0.577 -0.577 0.577 )
+DEAL::5: ( -0.394 -0.394 0.394 )
+DEAL::6: ( -0.707 0 0.707 )
+DEAL::7: ( -0.419 0 0.419 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.419 -0.419 0 )
+DEAL::1: ( -0.211 -0.211 0 )
+DEAL::2: ( -0.457 0 0 )
+DEAL::3: ( -0.211 0 0 )
+DEAL::4: ( -0.394 -0.394 0.394 )
+DEAL::5: ( -0.211 -0.211 0.211 )
+DEAL::6: ( -0.419 0 0.419 )
+DEAL::7: ( -0.211 0 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -1.00 0 0 )
+DEAL::1: ( -0.457 0 0 )
+DEAL::2: ( -0.707 0.707 0 )
+DEAL::3: ( -0.419 0.419 0 )
+DEAL::4: ( -0.707 0 0.707 )
+DEAL::5: ( -0.419 0 0.419 )
+DEAL::6: ( -0.577 0.577 0.577 )
+DEAL::7: ( -0.394 0.394 0.394 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.457 0 0 )
+DEAL::1: ( -0.211 0 0 )
+DEAL::2: ( -0.419 0.419 0 )
+DEAL::3: ( -0.211 0.211 0 )
+DEAL::4: ( -0.419 0 0.419 )
+DEAL::5: ( -0.211 0 0.211 )
+DEAL::6: ( -0.394 0.394 0.394 )
+DEAL::7: ( -0.211 0.211 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.577 -0.577 -0.577 )
+DEAL::1: ( 0 -0.707 -0.707 )
+DEAL::2: ( -0.394 -0.394 -0.394 )
+DEAL::3: ( 0 -0.419 -0.419 )
+DEAL::4: ( -0.707 -0.707 0 )
+DEAL::5: ( 0 -1.00 0 )
+DEAL::6: ( -0.419 -0.419 0 )
+DEAL::7: ( 0 -0.457 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 -0.707 -0.707 )
+DEAL::1: ( 0.577 -0.577 -0.577 )
+DEAL::2: ( 0 -0.419 -0.419 )
+DEAL::3: ( 0.394 -0.394 -0.394 )
+DEAL::4: ( 0 -1.00 0 )
+DEAL::5: ( 0.707 -0.707 0 )
+DEAL::6: ( 0 -0.457 0 )
+DEAL::7: ( 0.419 -0.419 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.394 -0.394 -0.394 )
+DEAL::1: ( 0 -0.419 -0.419 )
+DEAL::2: ( -0.211 -0.211 -0.211 )
+DEAL::3: ( 0 -0.211 -0.211 )
+DEAL::4: ( -0.419 -0.419 0 )
+DEAL::5: ( 0 -0.457 0 )
+DEAL::6: ( -0.211 -0.211 0 )
+DEAL::7: ( 0 -0.211 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 -0.419 -0.419 )
+DEAL::1: ( 0.394 -0.394 -0.394 )
+DEAL::2: ( 0 -0.211 -0.211 )
+DEAL::3: ( 0.211 -0.211 -0.211 )
+DEAL::4: ( 0 -0.457 0 )
+DEAL::5: ( 0.419 -0.419 0 )
+DEAL::6: ( 0 -0.211 0 )
+DEAL::7: ( 0.211 -0.211 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.707 -0.707 0 )
+DEAL::1: ( 0 -1.00 0 )
+DEAL::2: ( -0.419 -0.419 0 )
+DEAL::3: ( 0 -0.457 0 )
+DEAL::4: ( -0.577 -0.577 0.577 )
+DEAL::5: ( 0 -0.707 0.707 )
+DEAL::6: ( -0.394 -0.394 0.394 )
+DEAL::7: ( 0 -0.419 0.419 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 -1.00 0 )
+DEAL::1: ( 0.707 -0.707 0 )
+DEAL::2: ( 0 -0.457 0 )
+DEAL::3: ( 0.419 -0.419 0 )
+DEAL::4: ( 0 -0.707 0.707 )
+DEAL::5: ( 0.577 -0.577 0.577 )
+DEAL::6: ( 0 -0.419 0.419 )
+DEAL::7: ( 0.394 -0.394 0.394 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.419 -0.419 0 )
+DEAL::1: ( 0 -0.457 0 )
+DEAL::2: ( -0.211 -0.211 0 )
+DEAL::3: ( 0 -0.211 0 )
+DEAL::4: ( -0.394 -0.394 0.394 )
+DEAL::5: ( 0 -0.419 0.419 )
+DEAL::6: ( -0.211 -0.211 0.211 )
+DEAL::7: ( 0 -0.211 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 -0.457 0 )
+DEAL::1: ( 0.419 -0.419 0 )
+DEAL::2: ( 0 -0.211 0 )
+DEAL::3: ( 0.211 -0.211 0 )
+DEAL::4: ( 0 -0.419 0.419 )
+DEAL::5: ( 0.394 -0.394 0.394 )
+DEAL::6: ( 0 -0.211 0.211 )
+DEAL::7: ( 0.211 -0.211 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.577 0.577 -0.577 )
+DEAL::1: ( -0.394 0.394 -0.394 )
+DEAL::2: ( 0 0.707 -0.707 )
+DEAL::3: ( 0 0.419 -0.419 )
+DEAL::4: ( -0.707 0.707 0 )
+DEAL::5: ( -0.419 0.419 0 )
+DEAL::6: ( 0 1.00 0 )
+DEAL::7: ( 0 0.457 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.394 0.394 -0.394 )
+DEAL::1: ( -0.211 0.211 -0.211 )
+DEAL::2: ( 0 0.419 -0.419 )
+DEAL::3: ( 0 0.211 -0.211 )
+DEAL::4: ( -0.419 0.419 0 )
+DEAL::5: ( -0.211 0.211 0 )
+DEAL::6: ( 0 0.457 0 )
+DEAL::7: ( 0 0.211 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 0.707 -0.707 )
+DEAL::1: ( 0 0.419 -0.419 )
+DEAL::2: ( 0.577 0.577 -0.577 )
+DEAL::3: ( 0.394 0.394 -0.394 )
+DEAL::4: ( 0 1.00 0 )
+DEAL::5: ( 0 0.457 0 )
+DEAL::6: ( 0.707 0.707 0 )
+DEAL::7: ( 0.419 0.419 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 0.419 -0.419 )
+DEAL::1: ( 0 0.211 -0.211 )
+DEAL::2: ( 0.394 0.394 -0.394 )
+DEAL::3: ( 0.211 0.211 -0.211 )
+DEAL::4: ( 0 0.457 0 )
+DEAL::5: ( 0 0.211 0 )
+DEAL::6: ( 0.419 0.419 0 )
+DEAL::7: ( 0.211 0.211 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.707 0.707 0 )
+DEAL::1: ( -0.419 0.419 0 )
+DEAL::2: ( 0 1.00 0 )
+DEAL::3: ( 0 0.457 0 )
+DEAL::4: ( -0.577 0.577 0.577 )
+DEAL::5: ( -0.394 0.394 0.394 )
+DEAL::6: ( 0 0.707 0.707 )
+DEAL::7: ( 0 0.419 0.419 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.419 0.419 0 )
+DEAL::1: ( -0.211 0.211 0 )
+DEAL::2: ( 0 0.457 0 )
+DEAL::3: ( 0 0.211 0 )
+DEAL::4: ( -0.394 0.394 0.394 )
+DEAL::5: ( -0.211 0.211 0.211 )
+DEAL::6: ( 0 0.419 0.419 )
+DEAL::7: ( 0 0.211 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 1.00 0 )
+DEAL::1: ( 0 0.457 0 )
+DEAL::2: ( 0.707 0.707 0 )
+DEAL::3: ( 0.419 0.419 0 )
+DEAL::4: ( 0 0.707 0.707 )
+DEAL::5: ( 0 0.419 0.419 )
+DEAL::6: ( 0.577 0.577 0.577 )
+DEAL::7: ( 0.394 0.394 0.394 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 0.457 0 )
+DEAL::1: ( 0 0.211 0 )
+DEAL::2: ( 0.419 0.419 0 )
+DEAL::3: ( 0.211 0.211 0 )
+DEAL::4: ( 0 0.419 0.419 )
+DEAL::5: ( 0 0.211 0.211 )
+DEAL::6: ( 0.394 0.394 0.394 )
+DEAL::7: ( 0.211 0.211 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::done...

diff --git a/tests/fe/fe_dgq_3rd_derivative_divergence_theorem.cc b/tests/fe/fe_dgq_3rd_derivative_divergence_theorem.cc
new file mode 100644 (file)
index 0000000..4d47c20
--- /dev/null
+++ b/tests/fe/fe_dgq_3rd_derivative_divergence_theorem.cc
@@ -0,0 +1,176 @@
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2003 - 2015 by the deal.II authors
+//
+// This file is part of the deal.II library.
+//
+// The deal.II library is free software; you can use it, redistribute
+// it, and/or modify it under the terms of the GNU Lesser General
+// Public License as published by the Free Software Foundation; either
+// version 2.1 of the License, or (at your option) any later version.
+// The full text of the license can be found in the file LICENSE at
+// the top level of the deal.II distribution.
+//
+// ---------------------------------------------------------------------
+
+
+// check the correctness of fe_values.shape_3rd_derivative for FE_DGQ by comparing
+// the integral of all shape third derivative components with the flux of the
+// hessian over the boundary by the divergence theorem
+
+#include "../tests.h"
+#include <deal.II/base/logstream.h>
+#include <deal.II/base/function.h>
+#include <deal.II/base/quadrature_lib.h>
+#include <deal.II/lac/vector.h>
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/tria_boundary_lib.h>
+#include <deal.II/dofs/dof_handler.h>
+#include <deal.II/fe/fe_q.h>
+#include <deal.II/fe/fe_raviart_thomas.h>
+#include <deal.II/fe/fe_nedelec.h>
+#include <deal.II/fe/fe_dgq.h>
+#include <deal.II/fe/fe_system.h>
+#include <deal.II/fe/fe_values.h>
+#include <deal.II/fe/mapping_q1.h>
+
+#include <sstream>
+#include <fstream>
+
+template<int dim>
+Tensor<1,dim> ones ()
+{
+  Tensor<1,dim> result;
+  for (unsigned int i=0; i<dim; ++i)
+    result[i] = 1.0;
+  return result;
+}
+
+template<int dim>
+void test (const Triangulation<dim> &tr,
+           const FiniteElement<dim> &fe,
+           const double tolerance)
+{
+  DoFHandler<dim> dof(tr);
+  dof.distribute_dofs(fe);
+
+  std::stringstream ss;
+
+  deallog << "FE=" << fe.get_name() << std::endl;
+
+  const QGauss<dim> quadrature(6);
+  FEValues<dim> fe_values (fe, quadrature, update_3rd_derivatives
+                           | update_quadrature_points
+                           | update_JxW_values);
+
+  const QGauss<dim-1> face_quadrature(6);
+  FEFaceValues<dim> fe_face_values (fe, face_quadrature,
+                                    update_hessians
+                                    | update_quadrature_points
+                                    | update_normal_vectors
+                                    | update_JxW_values);
+
+  for (typename DoFHandler<dim>::active_cell_iterator cell = dof.begin_active();
+       cell != dof.end();
+       ++cell)
+    {
+      fe_values.reinit (cell);
+
+      deallog << "Cell nodes:" << std::endl;
+      for (unsigned int i=0; i<GeometryInfo<dim>::vertices_per_cell; ++i)
+        {
+          deallog << i << ": ( ";
+          for (unsigned int d=0; d<dim; ++d)
+            deallog << cell->vertex(i)[d] << " ";
+          deallog << ")" << std::endl;
+        }
+
+      bool cell_ok = true;
+
+      for (unsigned int c=0; c<fe.n_components(); ++c)
+        {
+          FEValuesExtractors::Scalar single_component (c);
+
+          for (unsigned int i=0; i<fe_values.dofs_per_cell; ++i)
+            {
+              ss << "component=" << c
+                 << ", dof=" << i
+                 << std::endl;
+
+              Tensor<3,dim> bulk_integral;
+              for (unsigned int q=0; q<fe_values.n_quadrature_points; ++q)
+                {
+                  bulk_integral += fe_values[single_component].third_derivative(i,q) * fe_values.JxW(q);
+
+                  Tensor<3,dim> third_derivative = fe_values[single_component].third_derivative(i,q);
+                }
+
+              Tensor<3,dim> boundary_integral;
+              for (unsigned int face=0; face<GeometryInfo<dim>::faces_per_cell; ++face)
+                {
+                  fe_face_values.reinit(cell,face);
+                  for (unsigned int q=0; q<fe_face_values.n_quadrature_points; ++q)
+                    {
+                      Tensor<2,dim> hessian = fe_face_values[single_component].hessian (i,q);
+                      Tensor<3,dim> hessian_normal_outer_prod;
+
+                      outer_product(hessian_normal_outer_prod, hessian, fe_face_values.normal_vector(q));
+                      boundary_integral += hessian_normal_outer_prod * fe_face_values.JxW(q);
+                    }
+                }
+
+              if ((bulk_integral-boundary_integral).norm_square() > tolerance * (bulk_integral.norm() + boundary_integral.norm()))
+                {
+                  deallog << "Failed:" << std::endl;
+                  deallog << ss.str() << std::endl;
+                  deallog << "    bulk integral=" << bulk_integral << std::endl;
+                  deallog << "boundary integral=" << boundary_integral << std::endl;
+                  deallog << "Error! difference between bulk and surface integrals is "
+                          << (bulk_integral-boundary_integral).norm_square()
+                          << " and greater than "
+                          << tolerance * (bulk_integral.norm() + boundary_integral.norm())
+                          << "!\n\n" << std::endl;
+                  cell_ok = false;
+                }
+
+              ss.str("");
+            }
+        }
+
+      deallog << (cell_ok? "OK: cell bulk and boundary integrals match...\n" : "Failed divergence test...\n") << std::endl;
+    }
+}
+
+
+
+template<int dim>
+void test_hyper_ball(const double tolerance)
+{
+  Triangulation<dim> tr;
+  GridGenerator::hyper_ball(tr);
+
+  static const HyperBallBoundary<dim> boundary;
+  tr.set_boundary (0, boundary);
+
+  tr.refine_global(1);
+
+  FE_DGQ<dim>  fe(2);
+  test(tr, fe, tolerance);
+}
+
+
+int main()
+{
+  std::ofstream logfile ("output");
+  deallog << std::setprecision (3);
+
+  deallog.attach(logfile);
+  deallog.depth_console (0);
+  deallog.threshold_double(1.e-7);
+
+  test_hyper_ball<2>(1e-6);
+  test_hyper_ball<3>(1e-6);
+
+  deallog << "done..." << std::endl;
+}
+

diff --git a/tests/fe/fe_dgq_3rd_derivative_divergence_theorem.output b/tests/fe/fe_dgq_3rd_derivative_divergence_theorem.output
new file mode 100644 (file)
index 0000000..1e607ed
--- /dev/null
+++ b/tests/fe/fe_dgq_3rd_derivative_divergence_theorem.output
@@ -0,0 +1,760 @@
+
+DEAL::FE=FE_DGQ<2>(2)
+DEAL::Cell nodes:
+DEAL::0: ( -0.707 -0.707 )
+DEAL::1: ( 0 -1.00 )
+DEAL::2: ( -0.500 -0.500 )
+DEAL::3: ( 0 -0.646 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 -1.00 )
+DEAL::1: ( 0.707 -0.707 )
+DEAL::2: ( 0 -0.646 )
+DEAL::3: ( 0.500 -0.500 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.500 -0.500 )
+DEAL::1: ( 0 -0.646 )
+DEAL::2: ( -0.293 -0.293 )
+DEAL::3: ( 0 -0.293 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 -0.646 )
+DEAL::1: ( 0.500 -0.500 )
+DEAL::2: ( 0 -0.293 )
+DEAL::3: ( 0.293 -0.293 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.707 -0.707 )
+DEAL::1: ( -0.500 -0.500 )
+DEAL::2: ( -1.00 0 )
+DEAL::3: ( -0.646 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.500 -0.500 )
+DEAL::1: ( -0.293 -0.293 )
+DEAL::2: ( -0.646 0 )
+DEAL::3: ( -0.293 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -1.00 0 )
+DEAL::1: ( -0.646 0 )
+DEAL::2: ( -0.707 0.707 )
+DEAL::3: ( -0.500 0.500 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.646 0 )
+DEAL::1: ( -0.293 0 )
+DEAL::2: ( -0.500 0.500 )
+DEAL::3: ( -0.293 0.293 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.293 -0.293 )
+DEAL::1: ( 0 -0.293 )
+DEAL::2: ( -0.293 0 )
+DEAL::3: ( 0 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 -0.293 )
+DEAL::1: ( 0.293 -0.293 )
+DEAL::2: ( 0 0 )
+DEAL::3: ( 0.293 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.293 0 )
+DEAL::1: ( 0 0 )
+DEAL::2: ( -0.293 0.293 )
+DEAL::3: ( 0 0.293 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 0 )
+DEAL::1: ( 0.293 0 )
+DEAL::2: ( 0 0.293 )
+DEAL::3: ( 0.293 0.293 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.707 -0.707 )
+DEAL::1: ( 1.00 0 )
+DEAL::2: ( 0.500 -0.500 )
+DEAL::3: ( 0.646 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 1.00 0 )
+DEAL::1: ( 0.707 0.707 )
+DEAL::2: ( 0.646 0 )
+DEAL::3: ( 0.500 0.500 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.500 -0.500 )
+DEAL::1: ( 0.646 0 )
+DEAL::2: ( 0.293 -0.293 )
+DEAL::3: ( 0.293 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.646 0 )
+DEAL::1: ( 0.500 0.500 )
+DEAL::2: ( 0.293 0 )
+DEAL::3: ( 0.293 0.293 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.707 0.707 )
+DEAL::1: ( -0.500 0.500 )
+DEAL::2: ( 0 1.00 )
+DEAL::3: ( 0 0.646 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.500 0.500 )
+DEAL::1: ( -0.293 0.293 )
+DEAL::2: ( 0 0.646 )
+DEAL::3: ( 0 0.293 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 1.00 )
+DEAL::1: ( 0 0.646 )
+DEAL::2: ( 0.707 0.707 )
+DEAL::3: ( 0.500 0.500 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 0.646 )
+DEAL::1: ( 0 0.293 )
+DEAL::2: ( 0.500 0.500 )
+DEAL::3: ( 0.293 0.293 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::FE=FE_DGQ<3>(2)
+DEAL::Cell nodes:
+DEAL::0: ( -0.211 -0.211 -0.211 )
+DEAL::1: ( 0 -0.211 -0.211 )
+DEAL::2: ( -0.211 0 -0.211 )
+DEAL::3: ( 0 0 -0.211 )
+DEAL::4: ( -0.211 -0.211 0 )
+DEAL::5: ( 0 -0.211 0 )
+DEAL::6: ( -0.211 0 0 )
+DEAL::7: ( 0 0 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 -0.211 -0.211 )
+DEAL::1: ( 0.211 -0.211 -0.211 )
+DEAL::2: ( 0 0 -0.211 )
+DEAL::3: ( 0.211 0 -0.211 )
+DEAL::4: ( 0 -0.211 0 )
+DEAL::5: ( 0.211 -0.211 0 )
+DEAL::6: ( 0 0 0 )
+DEAL::7: ( 0.211 0 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.211 0 -0.211 )
+DEAL::1: ( 0 0 -0.211 )
+DEAL::2: ( -0.211 0.211 -0.211 )
+DEAL::3: ( 0 0.211 -0.211 )
+DEAL::4: ( -0.211 0 0 )
+DEAL::5: ( 0 0 0 )
+DEAL::6: ( -0.211 0.211 0 )
+DEAL::7: ( 0 0.211 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 0 -0.211 )
+DEAL::1: ( 0.211 0 -0.211 )
+DEAL::2: ( 0 0.211 -0.211 )
+DEAL::3: ( 0.211 0.211 -0.211 )
+DEAL::4: ( 0 0 0 )
+DEAL::5: ( 0.211 0 0 )
+DEAL::6: ( 0 0.211 0 )
+DEAL::7: ( 0.211 0.211 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.211 -0.211 0 )
+DEAL::1: ( 0 -0.211 0 )
+DEAL::2: ( -0.211 0 0 )
+DEAL::3: ( 0 0 0 )
+DEAL::4: ( -0.211 -0.211 0.211 )
+DEAL::5: ( 0 -0.211 0.211 )
+DEAL::6: ( -0.211 0 0.211 )
+DEAL::7: ( 0 0 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 -0.211 0 )
+DEAL::1: ( 0.211 -0.211 0 )
+DEAL::2: ( 0 0 0 )
+DEAL::3: ( 0.211 0 0 )
+DEAL::4: ( 0 -0.211 0.211 )
+DEAL::5: ( 0.211 -0.211 0.211 )
+DEAL::6: ( 0 0 0.211 )
+DEAL::7: ( 0.211 0 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.211 0 0 )
+DEAL::1: ( 0 0 0 )
+DEAL::2: ( -0.211 0.211 0 )
+DEAL::3: ( 0 0.211 0 )
+DEAL::4: ( -0.211 0 0.211 )
+DEAL::5: ( 0 0 0.211 )
+DEAL::6: ( -0.211 0.211 0.211 )
+DEAL::7: ( 0 0.211 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 0 0 )
+DEAL::1: ( 0.211 0 0 )
+DEAL::2: ( 0 0.211 0 )
+DEAL::3: ( 0.211 0.211 0 )
+DEAL::4: ( 0 0 0.211 )
+DEAL::5: ( 0.211 0 0.211 )
+DEAL::6: ( 0 0.211 0.211 )
+DEAL::7: ( 0.211 0.211 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.577 -0.577 -0.577 )
+DEAL::1: ( 0 -0.707 -0.707 )
+DEAL::2: ( -0.707 0 -0.707 )
+DEAL::3: ( 0 0 -1.00 )
+DEAL::4: ( -0.394 -0.394 -0.394 )
+DEAL::5: ( 0 -0.419 -0.419 )
+DEAL::6: ( -0.419 0 -0.419 )
+DEAL::7: ( 0 0 -0.457 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 -0.707 -0.707 )
+DEAL::1: ( 0.577 -0.577 -0.577 )
+DEAL::2: ( 0 0 -1.00 )
+DEAL::3: ( 0.707 0 -0.707 )
+DEAL::4: ( 0 -0.419 -0.419 )
+DEAL::5: ( 0.394 -0.394 -0.394 )
+DEAL::6: ( 0 0 -0.457 )
+DEAL::7: ( 0.419 0 -0.419 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.707 0 -0.707 )
+DEAL::1: ( 0 0 -1.00 )
+DEAL::2: ( -0.577 0.577 -0.577 )
+DEAL::3: ( 0 0.707 -0.707 )
+DEAL::4: ( -0.419 0 -0.419 )
+DEAL::5: ( 0 0 -0.457 )
+DEAL::6: ( -0.394 0.394 -0.394 )
+DEAL::7: ( 0 0.419 -0.419 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 0 -1.00 )
+DEAL::1: ( 0.707 0 -0.707 )
+DEAL::2: ( 0 0.707 -0.707 )
+DEAL::3: ( 0.577 0.577 -0.577 )
+DEAL::4: ( 0 0 -0.457 )
+DEAL::5: ( 0.419 0 -0.419 )
+DEAL::6: ( 0 0.419 -0.419 )
+DEAL::7: ( 0.394 0.394 -0.394 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.394 -0.394 -0.394 )
+DEAL::1: ( 0 -0.419 -0.419 )
+DEAL::2: ( -0.419 0 -0.419 )
+DEAL::3: ( 0 0 -0.457 )
+DEAL::4: ( -0.211 -0.211 -0.211 )
+DEAL::5: ( 0 -0.211 -0.211 )
+DEAL::6: ( -0.211 0 -0.211 )
+DEAL::7: ( 0 0 -0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 -0.419 -0.419 )
+DEAL::1: ( 0.394 -0.394 -0.394 )
+DEAL::2: ( 0 0 -0.457 )
+DEAL::3: ( 0.419 0 -0.419 )
+DEAL::4: ( 0 -0.211 -0.211 )
+DEAL::5: ( 0.211 -0.211 -0.211 )
+DEAL::6: ( 0 0 -0.211 )
+DEAL::7: ( 0.211 0 -0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.419 0 -0.419 )
+DEAL::1: ( 0 0 -0.457 )
+DEAL::2: ( -0.394 0.394 -0.394 )
+DEAL::3: ( 0 0.419 -0.419 )
+DEAL::4: ( -0.211 0 -0.211 )
+DEAL::5: ( 0 0 -0.211 )
+DEAL::6: ( -0.211 0.211 -0.211 )
+DEAL::7: ( 0 0.211 -0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 0 -0.457 )
+DEAL::1: ( 0.419 0 -0.419 )
+DEAL::2: ( 0 0.419 -0.419 )
+DEAL::3: ( 0.394 0.394 -0.394 )
+DEAL::4: ( 0 0 -0.211 )
+DEAL::5: ( 0.211 0 -0.211 )
+DEAL::6: ( 0 0.211 -0.211 )
+DEAL::7: ( 0.211 0.211 -0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.577 -0.577 -0.577 )
+DEAL::1: ( 0.707 0 -0.707 )
+DEAL::2: ( 0.394 -0.394 -0.394 )
+DEAL::3: ( 0.419 0 -0.419 )
+DEAL::4: ( 0.707 -0.707 0 )
+DEAL::5: ( 1.00 0 0 )
+DEAL::6: ( 0.419 -0.419 0 )
+DEAL::7: ( 0.457 0 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.707 0 -0.707 )
+DEAL::1: ( 0.577 0.577 -0.577 )
+DEAL::2: ( 0.419 0 -0.419 )
+DEAL::3: ( 0.394 0.394 -0.394 )
+DEAL::4: ( 1.00 0 0 )
+DEAL::5: ( 0.707 0.707 0 )
+DEAL::6: ( 0.457 0 0 )
+DEAL::7: ( 0.419 0.419 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.394 -0.394 -0.394 )
+DEAL::1: ( 0.419 0 -0.419 )
+DEAL::2: ( 0.211 -0.211 -0.211 )
+DEAL::3: ( 0.211 0 -0.211 )
+DEAL::4: ( 0.419 -0.419 0 )
+DEAL::5: ( 0.457 0 0 )
+DEAL::6: ( 0.211 -0.211 0 )
+DEAL::7: ( 0.211 0 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.419 0 -0.419 )
+DEAL::1: ( 0.394 0.394 -0.394 )
+DEAL::2: ( 0.211 0 -0.211 )
+DEAL::3: ( 0.211 0.211 -0.211 )
+DEAL::4: ( 0.457 0 0 )
+DEAL::5: ( 0.419 0.419 0 )
+DEAL::6: ( 0.211 0 0 )
+DEAL::7: ( 0.211 0.211 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.707 -0.707 0 )
+DEAL::1: ( 1.00 0 0 )
+DEAL::2: ( 0.419 -0.419 0 )
+DEAL::3: ( 0.457 0 0 )
+DEAL::4: ( 0.577 -0.577 0.577 )
+DEAL::5: ( 0.707 0 0.707 )
+DEAL::6: ( 0.394 -0.394 0.394 )
+DEAL::7: ( 0.419 0 0.419 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 1.00 0 0 )
+DEAL::1: ( 0.707 0.707 0 )
+DEAL::2: ( 0.457 0 0 )
+DEAL::3: ( 0.419 0.419 0 )
+DEAL::4: ( 0.707 0 0.707 )
+DEAL::5: ( 0.577 0.577 0.577 )
+DEAL::6: ( 0.419 0 0.419 )
+DEAL::7: ( 0.394 0.394 0.394 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.419 -0.419 0 )
+DEAL::1: ( 0.457 0 0 )
+DEAL::2: ( 0.211 -0.211 0 )
+DEAL::3: ( 0.211 0 0 )
+DEAL::4: ( 0.394 -0.394 0.394 )
+DEAL::5: ( 0.419 0 0.419 )
+DEAL::6: ( 0.211 -0.211 0.211 )
+DEAL::7: ( 0.211 0 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.457 0 0 )
+DEAL::1: ( 0.419 0.419 0 )
+DEAL::2: ( 0.211 0 0 )
+DEAL::3: ( 0.211 0.211 0 )
+DEAL::4: ( 0.419 0 0.419 )
+DEAL::5: ( 0.394 0.394 0.394 )
+DEAL::6: ( 0.211 0 0.211 )
+DEAL::7: ( 0.211 0.211 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.577 -0.577 0.577 )
+DEAL::1: ( 0 -0.707 0.707 )
+DEAL::2: ( -0.394 -0.394 0.394 )
+DEAL::3: ( 0 -0.419 0.419 )
+DEAL::4: ( -0.707 0 0.707 )
+DEAL::5: ( 0 0 1.00 )
+DEAL::6: ( -0.419 0 0.419 )
+DEAL::7: ( 0 0 0.457 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 -0.707 0.707 )
+DEAL::1: ( 0.577 -0.577 0.577 )
+DEAL::2: ( 0 -0.419 0.419 )
+DEAL::3: ( 0.394 -0.394 0.394 )
+DEAL::4: ( 0 0 1.00 )
+DEAL::5: ( 0.707 0 0.707 )
+DEAL::6: ( 0 0 0.457 )
+DEAL::7: ( 0.419 0 0.419 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.394 -0.394 0.394 )
+DEAL::1: ( 0 -0.419 0.419 )
+DEAL::2: ( -0.211 -0.211 0.211 )
+DEAL::3: ( 0 -0.211 0.211 )
+DEAL::4: ( -0.419 0 0.419 )
+DEAL::5: ( 0 0 0.457 )
+DEAL::6: ( -0.211 0 0.211 )
+DEAL::7: ( 0 0 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 -0.419 0.419 )
+DEAL::1: ( 0.394 -0.394 0.394 )
+DEAL::2: ( 0 -0.211 0.211 )
+DEAL::3: ( 0.211 -0.211 0.211 )
+DEAL::4: ( 0 0 0.457 )
+DEAL::5: ( 0.419 0 0.419 )
+DEAL::6: ( 0 0 0.211 )
+DEAL::7: ( 0.211 0 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.707 0 0.707 )
+DEAL::1: ( 0 0 1.00 )
+DEAL::2: ( -0.419 0 0.419 )
+DEAL::3: ( 0 0 0.457 )
+DEAL::4: ( -0.577 0.577 0.577 )
+DEAL::5: ( 0 0.707 0.707 )
+DEAL::6: ( -0.394 0.394 0.394 )
+DEAL::7: ( 0 0.419 0.419 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 0 1.00 )
+DEAL::1: ( 0.707 0 0.707 )
+DEAL::2: ( 0 0 0.457 )
+DEAL::3: ( 0.419 0 0.419 )
+DEAL::4: ( 0 0.707 0.707 )
+DEAL::5: ( 0.577 0.577 0.577 )
+DEAL::6: ( 0 0.419 0.419 )
+DEAL::7: ( 0.394 0.394 0.394 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.419 0 0.419 )
+DEAL::1: ( 0 0 0.457 )
+DEAL::2: ( -0.211 0 0.211 )
+DEAL::3: ( 0 0 0.211 )
+DEAL::4: ( -0.394 0.394 0.394 )
+DEAL::5: ( 0 0.419 0.419 )
+DEAL::6: ( -0.211 0.211 0.211 )
+DEAL::7: ( 0 0.211 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 0 0.457 )
+DEAL::1: ( 0.419 0 0.419 )
+DEAL::2: ( 0 0 0.211 )
+DEAL::3: ( 0.211 0 0.211 )
+DEAL::4: ( 0 0.419 0.419 )
+DEAL::5: ( 0.394 0.394 0.394 )
+DEAL::6: ( 0 0.211 0.211 )
+DEAL::7: ( 0.211 0.211 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.577 -0.577 -0.577 )
+DEAL::1: ( -0.394 -0.394 -0.394 )
+DEAL::2: ( -0.707 0 -0.707 )
+DEAL::3: ( -0.419 0 -0.419 )
+DEAL::4: ( -0.707 -0.707 0 )
+DEAL::5: ( -0.419 -0.419 0 )
+DEAL::6: ( -1.00 0 0 )
+DEAL::7: ( -0.457 0 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.394 -0.394 -0.394 )
+DEAL::1: ( -0.211 -0.211 -0.211 )
+DEAL::2: ( -0.419 0 -0.419 )
+DEAL::3: ( -0.211 0 -0.211 )
+DEAL::4: ( -0.419 -0.419 0 )
+DEAL::5: ( -0.211 -0.211 0 )
+DEAL::6: ( -0.457 0 0 )
+DEAL::7: ( -0.211 0 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.707 0 -0.707 )
+DEAL::1: ( -0.419 0 -0.419 )
+DEAL::2: ( -0.577 0.577 -0.577 )
+DEAL::3: ( -0.394 0.394 -0.394 )
+DEAL::4: ( -1.00 0 0 )
+DEAL::5: ( -0.457 0 0 )
+DEAL::6: ( -0.707 0.707 0 )
+DEAL::7: ( -0.419 0.419 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.419 0 -0.419 )
+DEAL::1: ( -0.211 0 -0.211 )
+DEAL::2: ( -0.394 0.394 -0.394 )
+DEAL::3: ( -0.211 0.211 -0.211 )
+DEAL::4: ( -0.457 0 0 )
+DEAL::5: ( -0.211 0 0 )
+DEAL::6: ( -0.419 0.419 0 )
+DEAL::7: ( -0.211 0.211 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.707 -0.707 0 )
+DEAL::1: ( -0.419 -0.419 0 )
+DEAL::2: ( -1.00 0 0 )
+DEAL::3: ( -0.457 0 0 )
+DEAL::4: ( -0.577 -0.577 0.577 )
+DEAL::5: ( -0.394 -0.394 0.394 )
+DEAL::6: ( -0.707 0 0.707 )
+DEAL::7: ( -0.419 0 0.419 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.419 -0.419 0 )
+DEAL::1: ( -0.211 -0.211 0 )
+DEAL::2: ( -0.457 0 0 )
+DEAL::3: ( -0.211 0 0 )
+DEAL::4: ( -0.394 -0.394 0.394 )
+DEAL::5: ( -0.211 -0.211 0.211 )
+DEAL::6: ( -0.419 0 0.419 )
+DEAL::7: ( -0.211 0 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -1.00 0 0 )
+DEAL::1: ( -0.457 0 0 )
+DEAL::2: ( -0.707 0.707 0 )
+DEAL::3: ( -0.419 0.419 0 )
+DEAL::4: ( -0.707 0 0.707 )
+DEAL::5: ( -0.419 0 0.419 )
+DEAL::6: ( -0.577 0.577 0.577 )
+DEAL::7: ( -0.394 0.394 0.394 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.457 0 0 )
+DEAL::1: ( -0.211 0 0 )
+DEAL::2: ( -0.419 0.419 0 )
+DEAL::3: ( -0.211 0.211 0 )
+DEAL::4: ( -0.419 0 0.419 )
+DEAL::5: ( -0.211 0 0.211 )
+DEAL::6: ( -0.394 0.394 0.394 )
+DEAL::7: ( -0.211 0.211 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.577 -0.577 -0.577 )
+DEAL::1: ( 0 -0.707 -0.707 )
+DEAL::2: ( -0.394 -0.394 -0.394 )
+DEAL::3: ( 0 -0.419 -0.419 )
+DEAL::4: ( -0.707 -0.707 0 )
+DEAL::5: ( 0 -1.00 0 )
+DEAL::6: ( -0.419 -0.419 0 )
+DEAL::7: ( 0 -0.457 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 -0.707 -0.707 )
+DEAL::1: ( 0.577 -0.577 -0.577 )
+DEAL::2: ( 0 -0.419 -0.419 )
+DEAL::3: ( 0.394 -0.394 -0.394 )
+DEAL::4: ( 0 -1.00 0 )
+DEAL::5: ( 0.707 -0.707 0 )
+DEAL::6: ( 0 -0.457 0 )
+DEAL::7: ( 0.419 -0.419 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.394 -0.394 -0.394 )
+DEAL::1: ( 0 -0.419 -0.419 )
+DEAL::2: ( -0.211 -0.211 -0.211 )
+DEAL::3: ( 0 -0.211 -0.211 )
+DEAL::4: ( -0.419 -0.419 0 )
+DEAL::5: ( 0 -0.457 0 )
+DEAL::6: ( -0.211 -0.211 0 )
+DEAL::7: ( 0 -0.211 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 -0.419 -0.419 )
+DEAL::1: ( 0.394 -0.394 -0.394 )
+DEAL::2: ( 0 -0.211 -0.211 )
+DEAL::3: ( 0.211 -0.211 -0.211 )
+DEAL::4: ( 0 -0.457 0 )
+DEAL::5: ( 0.419 -0.419 0 )
+DEAL::6: ( 0 -0.211 0 )
+DEAL::7: ( 0.211 -0.211 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.707 -0.707 0 )
+DEAL::1: ( 0 -1.00 0 )
+DEAL::2: ( -0.419 -0.419 0 )
+DEAL::3: ( 0 -0.457 0 )
+DEAL::4: ( -0.577 -0.577 0.577 )
+DEAL::5: ( 0 -0.707 0.707 )
+DEAL::6: ( -0.394 -0.394 0.394 )
+DEAL::7: ( 0 -0.419 0.419 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 -1.00 0 )
+DEAL::1: ( 0.707 -0.707 0 )
+DEAL::2: ( 0 -0.457 0 )
+DEAL::3: ( 0.419 -0.419 0 )
+DEAL::4: ( 0 -0.707 0.707 )
+DEAL::5: ( 0.577 -0.577 0.577 )
+DEAL::6: ( 0 -0.419 0.419 )
+DEAL::7: ( 0.394 -0.394 0.394 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.419 -0.419 0 )
+DEAL::1: ( 0 -0.457 0 )
+DEAL::2: ( -0.211 -0.211 0 )
+DEAL::3: ( 0 -0.211 0 )
+DEAL::4: ( -0.394 -0.394 0.394 )
+DEAL::5: ( 0 -0.419 0.419 )
+DEAL::6: ( -0.211 -0.211 0.211 )
+DEAL::7: ( 0 -0.211 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 -0.457 0 )
+DEAL::1: ( 0.419 -0.419 0 )
+DEAL::2: ( 0 -0.211 0 )
+DEAL::3: ( 0.211 -0.211 0 )
+DEAL::4: ( 0 -0.419 0.419 )
+DEAL::5: ( 0.394 -0.394 0.394 )
+DEAL::6: ( 0 -0.211 0.211 )
+DEAL::7: ( 0.211 -0.211 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.577 0.577 -0.577 )
+DEAL::1: ( -0.394 0.394 -0.394 )
+DEAL::2: ( 0 0.707 -0.707 )
+DEAL::3: ( 0 0.419 -0.419 )
+DEAL::4: ( -0.707 0.707 0 )
+DEAL::5: ( -0.419 0.419 0 )
+DEAL::6: ( 0 1.00 0 )
+DEAL::7: ( 0 0.457 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.394 0.394 -0.394 )
+DEAL::1: ( -0.211 0.211 -0.211 )
+DEAL::2: ( 0 0.419 -0.419 )
+DEAL::3: ( 0 0.211 -0.211 )
+DEAL::4: ( -0.419 0.419 0 )
+DEAL::5: ( -0.211 0.211 0 )
+DEAL::6: ( 0 0.457 0 )
+DEAL::7: ( 0 0.211 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 0.707 -0.707 )
+DEAL::1: ( 0 0.419 -0.419 )
+DEAL::2: ( 0.577 0.577 -0.577 )
+DEAL::3: ( 0.394 0.394 -0.394 )
+DEAL::4: ( 0 1.00 0 )
+DEAL::5: ( 0 0.457 0 )
+DEAL::6: ( 0.707 0.707 0 )
+DEAL::7: ( 0.419 0.419 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 0.419 -0.419 )
+DEAL::1: ( 0 0.211 -0.211 )
+DEAL::2: ( 0.394 0.394 -0.394 )
+DEAL::3: ( 0.211 0.211 -0.211 )
+DEAL::4: ( 0 0.457 0 )
+DEAL::5: ( 0 0.211 0 )
+DEAL::6: ( 0.419 0.419 0 )
+DEAL::7: ( 0.211 0.211 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.707 0.707 0 )
+DEAL::1: ( -0.419 0.419 0 )
+DEAL::2: ( 0 1.00 0 )
+DEAL::3: ( 0 0.457 0 )
+DEAL::4: ( -0.577 0.577 0.577 )
+DEAL::5: ( -0.394 0.394 0.394 )
+DEAL::6: ( 0 0.707 0.707 )
+DEAL::7: ( 0 0.419 0.419 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.419 0.419 0 )
+DEAL::1: ( -0.211 0.211 0 )
+DEAL::2: ( 0 0.457 0 )
+DEAL::3: ( 0 0.211 0 )
+DEAL::4: ( -0.394 0.394 0.394 )
+DEAL::5: ( -0.211 0.211 0.211 )
+DEAL::6: ( 0 0.419 0.419 )
+DEAL::7: ( 0 0.211 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 1.00 0 )
+DEAL::1: ( 0 0.457 0 )
+DEAL::2: ( 0.707 0.707 0 )
+DEAL::3: ( 0.419 0.419 0 )
+DEAL::4: ( 0 0.707 0.707 )
+DEAL::5: ( 0 0.419 0.419 )
+DEAL::6: ( 0.577 0.577 0.577 )
+DEAL::7: ( 0.394 0.394 0.394 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 0.457 0 )
+DEAL::1: ( 0 0.211 0 )
+DEAL::2: ( 0.419 0.419 0 )
+DEAL::3: ( 0.211 0.211 0 )
+DEAL::4: ( 0 0.419 0.419 )
+DEAL::5: ( 0 0.211 0.211 )
+DEAL::6: ( 0.394 0.394 0.394 )
+DEAL::7: ( 0.211 0.211 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::done...

diff --git a/tests/fe/fe_q_hierarchical_3rd_derivative_divergence_theorem.cc b/tests/fe/fe_q_hierarchical_3rd_derivative_divergence_theorem.cc
new file mode 100644 (file)
index 0000000..2ca982f
--- /dev/null
+++ b/tests/fe/fe_q_hierarchical_3rd_derivative_divergence_theorem.cc
@@ -0,0 +1,177 @@
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2003 - 2015 by the deal.II authors
+//
+// This file is part of the deal.II library.
+//
+// The deal.II library is free software; you can use it, redistribute
+// it, and/or modify it under the terms of the GNU Lesser General
+// Public License as published by the Free Software Foundation; either
+// version 2.1 of the License, or (at your option) any later version.
+// The full text of the license can be found in the file LICENSE at
+// the top level of the deal.II distribution.
+//
+// ---------------------------------------------------------------------
+
+
+// check the correctness of fe_values.shape_3rd_derivative for FE_Q_Hierarchical by comparing
+// the integral of all shape third derivative components with the flux of the
+// hessian over the boundary by the divergence theorem
+
+#include "../tests.h"
+#include <deal.II/base/logstream.h>
+#include <deal.II/base/function.h>
+#include <deal.II/base/quadrature_lib.h>
+#include <deal.II/lac/vector.h>
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/tria_boundary_lib.h>
+#include <deal.II/dofs/dof_handler.h>
+#include <deal.II/fe/fe_q.h>
+#include <deal.II/fe/fe_q_hierarchical.h>
+#include <deal.II/fe/fe_raviart_thomas.h>
+#include <deal.II/fe/fe_nedelec.h>
+#include <deal.II/fe/fe_dgq.h>
+#include <deal.II/fe/fe_system.h>
+#include <deal.II/fe/fe_values.h>
+#include <deal.II/fe/mapping_q1.h>
+
+#include <sstream>
+#include <fstream>
+
+template<int dim>
+Tensor<1,dim> ones ()
+{
+  Tensor<1,dim> result;
+  for (unsigned int i=0; i<dim; ++i)
+    result[i] = 1.0;
+  return result;
+}
+
+template<int dim>
+void test (const Triangulation<dim> &tr,
+           const FiniteElement<dim> &fe,
+           const double tolerance)
+{
+  DoFHandler<dim> dof(tr);
+  dof.distribute_dofs(fe);
+
+  std::stringstream ss;
+
+  deallog << "FE=" << fe.get_name() << std::endl;
+
+  const QGauss<dim> quadrature(6);
+  FEValues<dim> fe_values (fe, quadrature, update_3rd_derivatives
+                           | update_quadrature_points
+                           | update_JxW_values);
+
+  const QGauss<dim-1> face_quadrature(6);
+  FEFaceValues<dim> fe_face_values (fe, face_quadrature,
+                                    update_hessians
+                                    | update_quadrature_points
+                                    | update_normal_vectors
+                                    | update_JxW_values);
+
+  for (typename DoFHandler<dim>::active_cell_iterator cell = dof.begin_active();
+       cell != dof.end();
+       ++cell)
+    {
+      fe_values.reinit (cell);
+
+      deallog << "Cell nodes:" << std::endl;
+      for (unsigned int i=0; i<GeometryInfo<dim>::vertices_per_cell; ++i)
+        {
+          deallog << i << ": ( ";
+          for (unsigned int d=0; d<dim; ++d)
+            deallog << cell->vertex(i)[d] << " ";
+          deallog << ")" << std::endl;
+        }
+
+      bool cell_ok = true;
+
+      for (unsigned int c=0; c<fe.n_components(); ++c)
+        {
+          FEValuesExtractors::Scalar single_component (c);
+
+          for (unsigned int i=0; i<fe_values.dofs_per_cell; ++i)
+            {
+              ss << "component=" << c
+                 << ", dof=" << i
+                 << std::endl;
+
+              Tensor<3,dim> bulk_integral;
+              for (unsigned int q=0; q<fe_values.n_quadrature_points; ++q)
+                {
+                  bulk_integral += fe_values[single_component].third_derivative(i,q) * fe_values.JxW(q);
+
+                  Tensor<3,dim> third_derivative = fe_values[single_component].third_derivative(i,q);
+                }
+
+              Tensor<3,dim> boundary_integral;
+              for (unsigned int face=0; face<GeometryInfo<dim>::faces_per_cell; ++face)
+                {
+                  fe_face_values.reinit(cell,face);
+                  for (unsigned int q=0; q<fe_face_values.n_quadrature_points; ++q)
+                    {
+                      Tensor<2,dim> hessian = fe_face_values[single_component].hessian (i,q);
+                      Tensor<3,dim> hessian_normal_outer_prod;
+
+                      outer_product(hessian_normal_outer_prod, hessian, fe_face_values.normal_vector(q));
+                      boundary_integral += hessian_normal_outer_prod * fe_face_values.JxW(q);
+                    }
+                }
+
+              if ((bulk_integral-boundary_integral).norm_square() > tolerance * (bulk_integral.norm() + boundary_integral.norm()))
+                {
+                  deallog << "Failed:" << std::endl;
+                  deallog << ss.str() << std::endl;
+                  deallog << "    bulk integral=" << bulk_integral << std::endl;
+                  deallog << "boundary integral=" << boundary_integral << std::endl;
+                  deallog << "Error! difference between bulk and surface integrals is "
+                          << (bulk_integral-boundary_integral).norm_square()
+                          << " and greater than "
+                          << tolerance * (bulk_integral.norm() + boundary_integral.norm())
+                          << "!\n\n" << std::endl;
+                  cell_ok = false;
+                }
+
+              ss.str("");
+            }
+        }
+
+      deallog << (cell_ok? "OK: cell bulk and boundary integrals match...\n" : "Failed divergence test...\n") << std::endl;
+    }
+}
+
+
+
+template<int dim>
+void test_hyper_ball(const double tolerance)
+{
+  Triangulation<dim> tr;
+  GridGenerator::hyper_ball(tr);
+
+  static const HyperBallBoundary<dim> boundary;
+  tr.set_boundary (0, boundary);
+
+  tr.refine_global(1);
+
+  FE_Q_Hierarchical<dim>  fe(2);
+  test(tr, fe, tolerance);
+}
+
+
+int main()
+{
+  std::ofstream logfile ("output");
+  deallog << std::setprecision (3);
+
+  deallog.attach(logfile);
+  deallog.depth_console (0);
+  deallog.threshold_double(1.e-7);
+
+  test_hyper_ball<2>(1e-6);
+  test_hyper_ball<3>(1e-6);
+
+  deallog << "done..." << std::endl;
+}
+

diff --git a/tests/fe/fe_q_hierarchical_3rd_derivative_divergence_theorem.output b/tests/fe/fe_q_hierarchical_3rd_derivative_divergence_theorem.output
new file mode 100644 (file)
index 0000000..f787888
--- /dev/null
+++ b/tests/fe/fe_q_hierarchical_3rd_derivative_divergence_theorem.output
@@ -0,0 +1,760 @@
+
+DEAL::FE=FE_Q_Hierarchical<2>(2)
+DEAL::Cell nodes:
+DEAL::0: ( -0.707 -0.707 )
+DEAL::1: ( 0 -1.00 )
+DEAL::2: ( -0.500 -0.500 )
+DEAL::3: ( 0 -0.646 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 -1.00 )
+DEAL::1: ( 0.707 -0.707 )
+DEAL::2: ( 0 -0.646 )
+DEAL::3: ( 0.500 -0.500 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.500 -0.500 )
+DEAL::1: ( 0 -0.646 )
+DEAL::2: ( -0.293 -0.293 )
+DEAL::3: ( 0 -0.293 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 -0.646 )
+DEAL::1: ( 0.500 -0.500 )
+DEAL::2: ( 0 -0.293 )
+DEAL::3: ( 0.293 -0.293 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.707 -0.707 )
+DEAL::1: ( -0.500 -0.500 )
+DEAL::2: ( -1.00 0 )
+DEAL::3: ( -0.646 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.500 -0.500 )
+DEAL::1: ( -0.293 -0.293 )
+DEAL::2: ( -0.646 0 )
+DEAL::3: ( -0.293 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -1.00 0 )
+DEAL::1: ( -0.646 0 )
+DEAL::2: ( -0.707 0.707 )
+DEAL::3: ( -0.500 0.500 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.646 0 )
+DEAL::1: ( -0.293 0 )
+DEAL::2: ( -0.500 0.500 )
+DEAL::3: ( -0.293 0.293 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.293 -0.293 )
+DEAL::1: ( 0 -0.293 )
+DEAL::2: ( -0.293 0 )
+DEAL::3: ( 0 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 -0.293 )
+DEAL::1: ( 0.293 -0.293 )
+DEAL::2: ( 0 0 )
+DEAL::3: ( 0.293 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.293 0 )
+DEAL::1: ( 0 0 )
+DEAL::2: ( -0.293 0.293 )
+DEAL::3: ( 0 0.293 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 0 )
+DEAL::1: ( 0.293 0 )
+DEAL::2: ( 0 0.293 )
+DEAL::3: ( 0.293 0.293 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.707 -0.707 )
+DEAL::1: ( 1.00 0 )
+DEAL::2: ( 0.500 -0.500 )
+DEAL::3: ( 0.646 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 1.00 0 )
+DEAL::1: ( 0.707 0.707 )
+DEAL::2: ( 0.646 0 )
+DEAL::3: ( 0.500 0.500 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.500 -0.500 )
+DEAL::1: ( 0.646 0 )
+DEAL::2: ( 0.293 -0.293 )
+DEAL::3: ( 0.293 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.646 0 )
+DEAL::1: ( 0.500 0.500 )
+DEAL::2: ( 0.293 0 )
+DEAL::3: ( 0.293 0.293 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.707 0.707 )
+DEAL::1: ( -0.500 0.500 )
+DEAL::2: ( 0 1.00 )
+DEAL::3: ( 0 0.646 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.500 0.500 )
+DEAL::1: ( -0.293 0.293 )
+DEAL::2: ( 0 0.646 )
+DEAL::3: ( 0 0.293 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 1.00 )
+DEAL::1: ( 0 0.646 )
+DEAL::2: ( 0.707 0.707 )
+DEAL::3: ( 0.500 0.500 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 0.646 )
+DEAL::1: ( 0 0.293 )
+DEAL::2: ( 0.500 0.500 )
+DEAL::3: ( 0.293 0.293 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::FE=FE_Q_Hierarchical<3>(2)
+DEAL::Cell nodes:
+DEAL::0: ( -0.211 -0.211 -0.211 )
+DEAL::1: ( 0 -0.211 -0.211 )
+DEAL::2: ( -0.211 0 -0.211 )
+DEAL::3: ( 0 0 -0.211 )
+DEAL::4: ( -0.211 -0.211 0 )
+DEAL::5: ( 0 -0.211 0 )
+DEAL::6: ( -0.211 0 0 )
+DEAL::7: ( 0 0 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 -0.211 -0.211 )
+DEAL::1: ( 0.211 -0.211 -0.211 )
+DEAL::2: ( 0 0 -0.211 )
+DEAL::3: ( 0.211 0 -0.211 )
+DEAL::4: ( 0 -0.211 0 )
+DEAL::5: ( 0.211 -0.211 0 )
+DEAL::6: ( 0 0 0 )
+DEAL::7: ( 0.211 0 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.211 0 -0.211 )
+DEAL::1: ( 0 0 -0.211 )
+DEAL::2: ( -0.211 0.211 -0.211 )
+DEAL::3: ( 0 0.211 -0.211 )
+DEAL::4: ( -0.211 0 0 )
+DEAL::5: ( 0 0 0 )
+DEAL::6: ( -0.211 0.211 0 )
+DEAL::7: ( 0 0.211 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 0 -0.211 )
+DEAL::1: ( 0.211 0 -0.211 )
+DEAL::2: ( 0 0.211 -0.211 )
+DEAL::3: ( 0.211 0.211 -0.211 )
+DEAL::4: ( 0 0 0 )
+DEAL::5: ( 0.211 0 0 )
+DEAL::6: ( 0 0.211 0 )
+DEAL::7: ( 0.211 0.211 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.211 -0.211 0 )
+DEAL::1: ( 0 -0.211 0 )
+DEAL::2: ( -0.211 0 0 )
+DEAL::3: ( 0 0 0 )
+DEAL::4: ( -0.211 -0.211 0.211 )
+DEAL::5: ( 0 -0.211 0.211 )
+DEAL::6: ( -0.211 0 0.211 )
+DEAL::7: ( 0 0 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 -0.211 0 )
+DEAL::1: ( 0.211 -0.211 0 )
+DEAL::2: ( 0 0 0 )
+DEAL::3: ( 0.211 0 0 )
+DEAL::4: ( 0 -0.211 0.211 )
+DEAL::5: ( 0.211 -0.211 0.211 )
+DEAL::6: ( 0 0 0.211 )
+DEAL::7: ( 0.211 0 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.211 0 0 )
+DEAL::1: ( 0 0 0 )
+DEAL::2: ( -0.211 0.211 0 )
+DEAL::3: ( 0 0.211 0 )
+DEAL::4: ( -0.211 0 0.211 )
+DEAL::5: ( 0 0 0.211 )
+DEAL::6: ( -0.211 0.211 0.211 )
+DEAL::7: ( 0 0.211 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 0 0 )
+DEAL::1: ( 0.211 0 0 )
+DEAL::2: ( 0 0.211 0 )
+DEAL::3: ( 0.211 0.211 0 )
+DEAL::4: ( 0 0 0.211 )
+DEAL::5: ( 0.211 0 0.211 )
+DEAL::6: ( 0 0.211 0.211 )
+DEAL::7: ( 0.211 0.211 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.577 -0.577 -0.577 )
+DEAL::1: ( 0 -0.707 -0.707 )
+DEAL::2: ( -0.707 0 -0.707 )
+DEAL::3: ( 0 0 -1.00 )
+DEAL::4: ( -0.394 -0.394 -0.394 )
+DEAL::5: ( 0 -0.419 -0.419 )
+DEAL::6: ( -0.419 0 -0.419 )
+DEAL::7: ( 0 0 -0.457 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 -0.707 -0.707 )
+DEAL::1: ( 0.577 -0.577 -0.577 )
+DEAL::2: ( 0 0 -1.00 )
+DEAL::3: ( 0.707 0 -0.707 )
+DEAL::4: ( 0 -0.419 -0.419 )
+DEAL::5: ( 0.394 -0.394 -0.394 )
+DEAL::6: ( 0 0 -0.457 )
+DEAL::7: ( 0.419 0 -0.419 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.707 0 -0.707 )
+DEAL::1: ( 0 0 -1.00 )
+DEAL::2: ( -0.577 0.577 -0.577 )
+DEAL::3: ( 0 0.707 -0.707 )
+DEAL::4: ( -0.419 0 -0.419 )
+DEAL::5: ( 0 0 -0.457 )
+DEAL::6: ( -0.394 0.394 -0.394 )
+DEAL::7: ( 0 0.419 -0.419 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 0 -1.00 )
+DEAL::1: ( 0.707 0 -0.707 )
+DEAL::2: ( 0 0.707 -0.707 )
+DEAL::3: ( 0.577 0.577 -0.577 )
+DEAL::4: ( 0 0 -0.457 )
+DEAL::5: ( 0.419 0 -0.419 )
+DEAL::6: ( 0 0.419 -0.419 )
+DEAL::7: ( 0.394 0.394 -0.394 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.394 -0.394 -0.394 )
+DEAL::1: ( 0 -0.419 -0.419 )
+DEAL::2: ( -0.419 0 -0.419 )
+DEAL::3: ( 0 0 -0.457 )
+DEAL::4: ( -0.211 -0.211 -0.211 )
+DEAL::5: ( 0 -0.211 -0.211 )
+DEAL::6: ( -0.211 0 -0.211 )
+DEAL::7: ( 0 0 -0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 -0.419 -0.419 )
+DEAL::1: ( 0.394 -0.394 -0.394 )
+DEAL::2: ( 0 0 -0.457 )
+DEAL::3: ( 0.419 0 -0.419 )
+DEAL::4: ( 0 -0.211 -0.211 )
+DEAL::5: ( 0.211 -0.211 -0.211 )
+DEAL::6: ( 0 0 -0.211 )
+DEAL::7: ( 0.211 0 -0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.419 0 -0.419 )
+DEAL::1: ( 0 0 -0.457 )
+DEAL::2: ( -0.394 0.394 -0.394 )
+DEAL::3: ( 0 0.419 -0.419 )
+DEAL::4: ( -0.211 0 -0.211 )
+DEAL::5: ( 0 0 -0.211 )
+DEAL::6: ( -0.211 0.211 -0.211 )
+DEAL::7: ( 0 0.211 -0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 0 -0.457 )
+DEAL::1: ( 0.419 0 -0.419 )
+DEAL::2: ( 0 0.419 -0.419 )
+DEAL::3: ( 0.394 0.394 -0.394 )
+DEAL::4: ( 0 0 -0.211 )
+DEAL::5: ( 0.211 0 -0.211 )
+DEAL::6: ( 0 0.211 -0.211 )
+DEAL::7: ( 0.211 0.211 -0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.577 -0.577 -0.577 )
+DEAL::1: ( 0.707 0 -0.707 )
+DEAL::2: ( 0.394 -0.394 -0.394 )
+DEAL::3: ( 0.419 0 -0.419 )
+DEAL::4: ( 0.707 -0.707 0 )
+DEAL::5: ( 1.00 0 0 )
+DEAL::6: ( 0.419 -0.419 0 )
+DEAL::7: ( 0.457 0 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.707 0 -0.707 )
+DEAL::1: ( 0.577 0.577 -0.577 )
+DEAL::2: ( 0.419 0 -0.419 )
+DEAL::3: ( 0.394 0.394 -0.394 )
+DEAL::4: ( 1.00 0 0 )
+DEAL::5: ( 0.707 0.707 0 )
+DEAL::6: ( 0.457 0 0 )
+DEAL::7: ( 0.419 0.419 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.394 -0.394 -0.394 )
+DEAL::1: ( 0.419 0 -0.419 )
+DEAL::2: ( 0.211 -0.211 -0.211 )
+DEAL::3: ( 0.211 0 -0.211 )
+DEAL::4: ( 0.419 -0.419 0 )
+DEAL::5: ( 0.457 0 0 )
+DEAL::6: ( 0.211 -0.211 0 )
+DEAL::7: ( 0.211 0 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.419 0 -0.419 )
+DEAL::1: ( 0.394 0.394 -0.394 )
+DEAL::2: ( 0.211 0 -0.211 )
+DEAL::3: ( 0.211 0.211 -0.211 )
+DEAL::4: ( 0.457 0 0 )
+DEAL::5: ( 0.419 0.419 0 )
+DEAL::6: ( 0.211 0 0 )
+DEAL::7: ( 0.211 0.211 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.707 -0.707 0 )
+DEAL::1: ( 1.00 0 0 )
+DEAL::2: ( 0.419 -0.419 0 )
+DEAL::3: ( 0.457 0 0 )
+DEAL::4: ( 0.577 -0.577 0.577 )
+DEAL::5: ( 0.707 0 0.707 )
+DEAL::6: ( 0.394 -0.394 0.394 )
+DEAL::7: ( 0.419 0 0.419 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 1.00 0 0 )
+DEAL::1: ( 0.707 0.707 0 )
+DEAL::2: ( 0.457 0 0 )
+DEAL::3: ( 0.419 0.419 0 )
+DEAL::4: ( 0.707 0 0.707 )
+DEAL::5: ( 0.577 0.577 0.577 )
+DEAL::6: ( 0.419 0 0.419 )
+DEAL::7: ( 0.394 0.394 0.394 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.419 -0.419 0 )
+DEAL::1: ( 0.457 0 0 )
+DEAL::2: ( 0.211 -0.211 0 )
+DEAL::3: ( 0.211 0 0 )
+DEAL::4: ( 0.394 -0.394 0.394 )
+DEAL::5: ( 0.419 0 0.419 )
+DEAL::6: ( 0.211 -0.211 0.211 )
+DEAL::7: ( 0.211 0 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.457 0 0 )
+DEAL::1: ( 0.419 0.419 0 )
+DEAL::2: ( 0.211 0 0 )
+DEAL::3: ( 0.211 0.211 0 )
+DEAL::4: ( 0.419 0 0.419 )
+DEAL::5: ( 0.394 0.394 0.394 )
+DEAL::6: ( 0.211 0 0.211 )
+DEAL::7: ( 0.211 0.211 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.577 -0.577 0.577 )
+DEAL::1: ( 0 -0.707 0.707 )
+DEAL::2: ( -0.394 -0.394 0.394 )
+DEAL::3: ( 0 -0.419 0.419 )
+DEAL::4: ( -0.707 0 0.707 )
+DEAL::5: ( 0 0 1.00 )
+DEAL::6: ( -0.419 0 0.419 )
+DEAL::7: ( 0 0 0.457 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 -0.707 0.707 )
+DEAL::1: ( 0.577 -0.577 0.577 )
+DEAL::2: ( 0 -0.419 0.419 )
+DEAL::3: ( 0.394 -0.394 0.394 )
+DEAL::4: ( 0 0 1.00 )
+DEAL::5: ( 0.707 0 0.707 )
+DEAL::6: ( 0 0 0.457 )
+DEAL::7: ( 0.419 0 0.419 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.394 -0.394 0.394 )
+DEAL::1: ( 0 -0.419 0.419 )
+DEAL::2: ( -0.211 -0.211 0.211 )
+DEAL::3: ( 0 -0.211 0.211 )
+DEAL::4: ( -0.419 0 0.419 )
+DEAL::5: ( 0 0 0.457 )
+DEAL::6: ( -0.211 0 0.211 )
+DEAL::7: ( 0 0 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 -0.419 0.419 )
+DEAL::1: ( 0.394 -0.394 0.394 )
+DEAL::2: ( 0 -0.211 0.211 )
+DEAL::3: ( 0.211 -0.211 0.211 )
+DEAL::4: ( 0 0 0.457 )
+DEAL::5: ( 0.419 0 0.419 )
+DEAL::6: ( 0 0 0.211 )
+DEAL::7: ( 0.211 0 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.707 0 0.707 )
+DEAL::1: ( 0 0 1.00 )
+DEAL::2: ( -0.419 0 0.419 )
+DEAL::3: ( 0 0 0.457 )
+DEAL::4: ( -0.577 0.577 0.577 )
+DEAL::5: ( 0 0.707 0.707 )
+DEAL::6: ( -0.394 0.394 0.394 )
+DEAL::7: ( 0 0.419 0.419 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 0 1.00 )
+DEAL::1: ( 0.707 0 0.707 )
+DEAL::2: ( 0 0 0.457 )
+DEAL::3: ( 0.419 0 0.419 )
+DEAL::4: ( 0 0.707 0.707 )
+DEAL::5: ( 0.577 0.577 0.577 )
+DEAL::6: ( 0 0.419 0.419 )
+DEAL::7: ( 0.394 0.394 0.394 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.419 0 0.419 )
+DEAL::1: ( 0 0 0.457 )
+DEAL::2: ( -0.211 0 0.211 )
+DEAL::3: ( 0 0 0.211 )
+DEAL::4: ( -0.394 0.394 0.394 )
+DEAL::5: ( 0 0.419 0.419 )
+DEAL::6: ( -0.211 0.211 0.211 )
+DEAL::7: ( 0 0.211 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 0 0.457 )
+DEAL::1: ( 0.419 0 0.419 )
+DEAL::2: ( 0 0 0.211 )
+DEAL::3: ( 0.211 0 0.211 )
+DEAL::4: ( 0 0.419 0.419 )
+DEAL::5: ( 0.394 0.394 0.394 )
+DEAL::6: ( 0 0.211 0.211 )
+DEAL::7: ( 0.211 0.211 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.577 -0.577 -0.577 )
+DEAL::1: ( -0.394 -0.394 -0.394 )
+DEAL::2: ( -0.707 0 -0.707 )
+DEAL::3: ( -0.419 0 -0.419 )
+DEAL::4: ( -0.707 -0.707 0 )
+DEAL::5: ( -0.419 -0.419 0 )
+DEAL::6: ( -1.00 0 0 )
+DEAL::7: ( -0.457 0 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.394 -0.394 -0.394 )
+DEAL::1: ( -0.211 -0.211 -0.211 )
+DEAL::2: ( -0.419 0 -0.419 )
+DEAL::3: ( -0.211 0 -0.211 )
+DEAL::4: ( -0.419 -0.419 0 )
+DEAL::5: ( -0.211 -0.211 0 )
+DEAL::6: ( -0.457 0 0 )
+DEAL::7: ( -0.211 0 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.707 0 -0.707 )
+DEAL::1: ( -0.419 0 -0.419 )
+DEAL::2: ( -0.577 0.577 -0.577 )
+DEAL::3: ( -0.394 0.394 -0.394 )
+DEAL::4: ( -1.00 0 0 )
+DEAL::5: ( -0.457 0 0 )
+DEAL::6: ( -0.707 0.707 0 )
+DEAL::7: ( -0.419 0.419 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.419 0 -0.419 )
+DEAL::1: ( -0.211 0 -0.211 )
+DEAL::2: ( -0.394 0.394 -0.394 )
+DEAL::3: ( -0.211 0.211 -0.211 )
+DEAL::4: ( -0.457 0 0 )
+DEAL::5: ( -0.211 0 0 )
+DEAL::6: ( -0.419 0.419 0 )
+DEAL::7: ( -0.211 0.211 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.707 -0.707 0 )
+DEAL::1: ( -0.419 -0.419 0 )
+DEAL::2: ( -1.00 0 0 )
+DEAL::3: ( -0.457 0 0 )
+DEAL::4: ( -0.577 -0.577 0.577 )
+DEAL::5: ( -0.394 -0.394 0.394 )
+DEAL::6: ( -0.707 0 0.707 )
+DEAL::7: ( -0.419 0 0.419 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.419 -0.419 0 )
+DEAL::1: ( -0.211 -0.211 0 )
+DEAL::2: ( -0.457 0 0 )
+DEAL::3: ( -0.211 0 0 )
+DEAL::4: ( -0.394 -0.394 0.394 )
+DEAL::5: ( -0.211 -0.211 0.211 )
+DEAL::6: ( -0.419 0 0.419 )
+DEAL::7: ( -0.211 0 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -1.00 0 0 )
+DEAL::1: ( -0.457 0 0 )
+DEAL::2: ( -0.707 0.707 0 )
+DEAL::3: ( -0.419 0.419 0 )
+DEAL::4: ( -0.707 0 0.707 )
+DEAL::5: ( -0.419 0 0.419 )
+DEAL::6: ( -0.577 0.577 0.577 )
+DEAL::7: ( -0.394 0.394 0.394 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.457 0 0 )
+DEAL::1: ( -0.211 0 0 )
+DEAL::2: ( -0.419 0.419 0 )
+DEAL::3: ( -0.211 0.211 0 )
+DEAL::4: ( -0.419 0 0.419 )
+DEAL::5: ( -0.211 0 0.211 )
+DEAL::6: ( -0.394 0.394 0.394 )
+DEAL::7: ( -0.211 0.211 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.577 -0.577 -0.577 )
+DEAL::1: ( 0 -0.707 -0.707 )
+DEAL::2: ( -0.394 -0.394 -0.394 )
+DEAL::3: ( 0 -0.419 -0.419 )
+DEAL::4: ( -0.707 -0.707 0 )
+DEAL::5: ( 0 -1.00 0 )
+DEAL::6: ( -0.419 -0.419 0 )
+DEAL::7: ( 0 -0.457 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 -0.707 -0.707 )
+DEAL::1: ( 0.577 -0.577 -0.577 )
+DEAL::2: ( 0 -0.419 -0.419 )
+DEAL::3: ( 0.394 -0.394 -0.394 )
+DEAL::4: ( 0 -1.00 0 )
+DEAL::5: ( 0.707 -0.707 0 )
+DEAL::6: ( 0 -0.457 0 )
+DEAL::7: ( 0.419 -0.419 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.394 -0.394 -0.394 )
+DEAL::1: ( 0 -0.419 -0.419 )
+DEAL::2: ( -0.211 -0.211 -0.211 )
+DEAL::3: ( 0 -0.211 -0.211 )
+DEAL::4: ( -0.419 -0.419 0 )
+DEAL::5: ( 0 -0.457 0 )
+DEAL::6: ( -0.211 -0.211 0 )
+DEAL::7: ( 0 -0.211 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 -0.419 -0.419 )
+DEAL::1: ( 0.394 -0.394 -0.394 )
+DEAL::2: ( 0 -0.211 -0.211 )
+DEAL::3: ( 0.211 -0.211 -0.211 )
+DEAL::4: ( 0 -0.457 0 )
+DEAL::5: ( 0.419 -0.419 0 )
+DEAL::6: ( 0 -0.211 0 )
+DEAL::7: ( 0.211 -0.211 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.707 -0.707 0 )
+DEAL::1: ( 0 -1.00 0 )
+DEAL::2: ( -0.419 -0.419 0 )
+DEAL::3: ( 0 -0.457 0 )
+DEAL::4: ( -0.577 -0.577 0.577 )
+DEAL::5: ( 0 -0.707 0.707 )
+DEAL::6: ( -0.394 -0.394 0.394 )
+DEAL::7: ( 0 -0.419 0.419 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 -1.00 0 )
+DEAL::1: ( 0.707 -0.707 0 )
+DEAL::2: ( 0 -0.457 0 )
+DEAL::3: ( 0.419 -0.419 0 )
+DEAL::4: ( 0 -0.707 0.707 )
+DEAL::5: ( 0.577 -0.577 0.577 )
+DEAL::6: ( 0 -0.419 0.419 )
+DEAL::7: ( 0.394 -0.394 0.394 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.419 -0.419 0 )
+DEAL::1: ( 0 -0.457 0 )
+DEAL::2: ( -0.211 -0.211 0 )
+DEAL::3: ( 0 -0.211 0 )
+DEAL::4: ( -0.394 -0.394 0.394 )
+DEAL::5: ( 0 -0.419 0.419 )
+DEAL::6: ( -0.211 -0.211 0.211 )
+DEAL::7: ( 0 -0.211 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 -0.457 0 )
+DEAL::1: ( 0.419 -0.419 0 )
+DEAL::2: ( 0 -0.211 0 )
+DEAL::3: ( 0.211 -0.211 0 )
+DEAL::4: ( 0 -0.419 0.419 )
+DEAL::5: ( 0.394 -0.394 0.394 )
+DEAL::6: ( 0 -0.211 0.211 )
+DEAL::7: ( 0.211 -0.211 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.577 0.577 -0.577 )
+DEAL::1: ( -0.394 0.394 -0.394 )
+DEAL::2: ( 0 0.707 -0.707 )
+DEAL::3: ( 0 0.419 -0.419 )
+DEAL::4: ( -0.707 0.707 0 )
+DEAL::5: ( -0.419 0.419 0 )
+DEAL::6: ( 0 1.00 0 )
+DEAL::7: ( 0 0.457 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.394 0.394 -0.394 )
+DEAL::1: ( -0.211 0.211 -0.211 )
+DEAL::2: ( 0 0.419 -0.419 )
+DEAL::3: ( 0 0.211 -0.211 )
+DEAL::4: ( -0.419 0.419 0 )
+DEAL::5: ( -0.211 0.211 0 )
+DEAL::6: ( 0 0.457 0 )
+DEAL::7: ( 0 0.211 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 0.707 -0.707 )
+DEAL::1: ( 0 0.419 -0.419 )
+DEAL::2: ( 0.577 0.577 -0.577 )
+DEAL::3: ( 0.394 0.394 -0.394 )
+DEAL::4: ( 0 1.00 0 )
+DEAL::5: ( 0 0.457 0 )
+DEAL::6: ( 0.707 0.707 0 )
+DEAL::7: ( 0.419 0.419 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 0.419 -0.419 )
+DEAL::1: ( 0 0.211 -0.211 )
+DEAL::2: ( 0.394 0.394 -0.394 )
+DEAL::3: ( 0.211 0.211 -0.211 )
+DEAL::4: ( 0 0.457 0 )
+DEAL::5: ( 0 0.211 0 )
+DEAL::6: ( 0.419 0.419 0 )
+DEAL::7: ( 0.211 0.211 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.707 0.707 0 )
+DEAL::1: ( -0.419 0.419 0 )
+DEAL::2: ( 0 1.00 0 )
+DEAL::3: ( 0 0.457 0 )
+DEAL::4: ( -0.577 0.577 0.577 )
+DEAL::5: ( -0.394 0.394 0.394 )
+DEAL::6: ( 0 0.707 0.707 )
+DEAL::7: ( 0 0.419 0.419 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.419 0.419 0 )
+DEAL::1: ( -0.211 0.211 0 )
+DEAL::2: ( 0 0.457 0 )
+DEAL::3: ( 0 0.211 0 )
+DEAL::4: ( -0.394 0.394 0.394 )
+DEAL::5: ( -0.211 0.211 0.211 )
+DEAL::6: ( 0 0.419 0.419 )
+DEAL::7: ( 0 0.211 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 1.00 0 )
+DEAL::1: ( 0 0.457 0 )
+DEAL::2: ( 0.707 0.707 0 )
+DEAL::3: ( 0.419 0.419 0 )
+DEAL::4: ( 0 0.707 0.707 )
+DEAL::5: ( 0 0.419 0.419 )
+DEAL::6: ( 0.577 0.577 0.577 )
+DEAL::7: ( 0.394 0.394 0.394 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 0.457 0 )
+DEAL::1: ( 0 0.211 0 )
+DEAL::2: ( 0.419 0.419 0 )
+DEAL::3: ( 0.211 0.211 0 )
+DEAL::4: ( 0 0.419 0.419 )
+DEAL::5: ( 0 0.211 0.211 )
+DEAL::6: ( 0.394 0.394 0.394 )
+DEAL::7: ( 0.211 0.211 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::done...

diff --git a/tests/fe/fe_system_3rd_derivative_divergence_theorem.cc b/tests/fe/fe_system_3rd_derivative_divergence_theorem.cc
new file mode 100644 (file)
index 0000000..22a6a02
--- /dev/null
+++ b/tests/fe/fe_system_3rd_derivative_divergence_theorem.cc
@@ -0,0 +1,176 @@
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2003 - 2015 by the deal.II authors
+//
+// This file is part of the deal.II library.
+//
+// The deal.II library is free software; you can use it, redistribute
+// it, and/or modify it under the terms of the GNU Lesser General
+// Public License as published by the Free Software Foundation; either
+// version 2.1 of the License, or (at your option) any later version.
+// The full text of the license can be found in the file LICENSE at
+// the top level of the deal.II distribution.
+//
+// ---------------------------------------------------------------------
+
+
+// check the correctness of fe_values.shape_3rd_derivative for FE_System by comparing
+// the integral of all shape third derivative components with the flux of the
+// hessian over the boundary by the divergence theorem
+
+#include "../tests.h"
+#include <deal.II/base/logstream.h>
+#include <deal.II/base/function.h>
+#include <deal.II/base/quadrature_lib.h>
+#include <deal.II/lac/vector.h>
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/tria_boundary_lib.h>
+#include <deal.II/dofs/dof_handler.h>
+#include <deal.II/fe/fe_q.h>
+#include <deal.II/fe/fe_raviart_thomas.h>
+#include <deal.II/fe/fe_nedelec.h>
+#include <deal.II/fe/fe_dgq.h>
+#include <deal.II/fe/fe_system.h>
+#include <deal.II/fe/fe_values.h>
+#include <deal.II/fe/mapping_q1.h>
+
+#include <sstream>
+#include <fstream>
+
+template<int dim>
+Tensor<1,dim> ones ()
+{
+  Tensor<1,dim> result;
+  for (unsigned int i=0; i<dim; ++i)
+    result[i] = 1.0;
+  return result;
+}
+
+template<int dim>
+void test (const Triangulation<dim> &tr,
+           const FiniteElement<dim> &fe,
+           const double tolerance)
+{
+  DoFHandler<dim> dof(tr);
+  dof.distribute_dofs(fe);
+
+  std::stringstream ss;
+
+  deallog << "FE=" << fe.get_name() << std::endl;
+
+  const QGauss<dim> quadrature(6);
+  FEValues<dim> fe_values (fe, quadrature, update_3rd_derivatives
+                           | update_quadrature_points
+                           | update_JxW_values);
+
+  const QGauss<dim-1> face_quadrature(6);
+  FEFaceValues<dim> fe_face_values (fe, face_quadrature,
+                                    update_hessians
+                                    | update_quadrature_points
+                                    | update_normal_vectors
+                                    | update_JxW_values);
+
+  for (typename DoFHandler<dim>::active_cell_iterator cell = dof.begin_active();
+       cell != dof.end();
+       ++cell)
+    {
+      fe_values.reinit (cell);
+
+      deallog << "Cell nodes:" << std::endl;
+      for (unsigned int i=0; i<GeometryInfo<dim>::vertices_per_cell; ++i)
+        {
+          deallog << i << ": ( ";
+          for (unsigned int d=0; d<dim; ++d)
+            deallog << cell->vertex(i)[d] << " ";
+          deallog << ")" << std::endl;
+        }
+
+      bool cell_ok = true;
+
+      for (unsigned int c=0; c<fe.n_components(); ++c)
+        {
+          FEValuesExtractors::Scalar single_component (c);
+
+          for (unsigned int i=0; i<fe_values.dofs_per_cell; ++i)
+            {
+              ss << "component=" << c
+                 << ", dof=" << i
+                 << std::endl;
+
+              Tensor<3,dim> bulk_integral;
+              for (unsigned int q=0; q<fe_values.n_quadrature_points; ++q)
+                {
+                  bulk_integral += fe_values[single_component].third_derivative(i,q) * fe_values.JxW(q);
+
+                  Tensor<3,dim> third_derivative = fe_values[single_component].third_derivative(i,q);
+                }
+
+              Tensor<3,dim> boundary_integral;
+              for (unsigned int face=0; face<GeometryInfo<dim>::faces_per_cell; ++face)
+                {
+                  fe_face_values.reinit(cell,face);
+                  for (unsigned int q=0; q<fe_face_values.n_quadrature_points; ++q)
+                    {
+                      Tensor<2,dim> hessian = fe_face_values[single_component].hessian (i,q);
+                      Tensor<3,dim> hessian_normal_outer_prod;
+
+                      outer_product(hessian_normal_outer_prod, hessian, fe_face_values.normal_vector(q));
+                      boundary_integral += hessian_normal_outer_prod * fe_face_values.JxW(q);
+                    }
+                }
+
+              if ((bulk_integral-boundary_integral).norm_square() > tolerance * (bulk_integral.norm() + boundary_integral.norm()))
+                {
+                  deallog << "Failed:" << std::endl;
+                  deallog << ss.str() << std::endl;
+                  deallog << "    bulk integral=" << bulk_integral << std::endl;
+                  deallog << "boundary integral=" << boundary_integral << std::endl;
+                  deallog << "Error! difference between bulk and surface integrals is "
+                          << (bulk_integral-boundary_integral).norm_square()
+                          << " and greater than "
+                          << tolerance * (bulk_integral.norm() + boundary_integral.norm())
+                          << "!\n\n" << std::endl;
+                  cell_ok = false;
+                }
+
+              ss.str("");
+            }
+        }
+
+      deallog << (cell_ok? "OK: cell bulk and boundary integrals match...\n" : "Failed divergence test...\n") << std::endl;
+    }
+}
+
+
+
+template<int dim>
+void test_hyper_ball(const double tolerance)
+{
+  Triangulation<dim> tr;
+  GridGenerator::hyper_ball(tr);
+
+  static const HyperBallBoundary<dim> boundary;
+  tr.set_boundary (0, boundary);
+
+  tr.refine_global(1);
+
+  FESystem<dim>  fe(FE_Q<dim>(2),1);
+  test(tr, fe, tolerance);
+}
+
+
+int main()
+{
+  std::ofstream logfile ("output");
+  deallog << std::setprecision (3);
+
+  deallog.attach(logfile);
+  deallog.depth_console (0);
+  deallog.threshold_double(1.e-7);
+
+  test_hyper_ball<2>(1e-6);
+  test_hyper_ball<3>(1e-6);
+
+  deallog << "done..." << std::endl;
+}
+

diff --git a/tests/fe/fe_system_3rd_derivative_divergence_theorem.output b/tests/fe/fe_system_3rd_derivative_divergence_theorem.output
new file mode 100644 (file)
index 0000000..0b72854
--- /dev/null
+++ b/tests/fe/fe_system_3rd_derivative_divergence_theorem.output
@@ -0,0 +1,760 @@
+
+DEAL::FE=FESystem<2>[FE_Q<2>(2)]
+DEAL::Cell nodes:
+DEAL::0: ( -0.707 -0.707 )
+DEAL::1: ( 0 -1.00 )
+DEAL::2: ( -0.500 -0.500 )
+DEAL::3: ( 0 -0.646 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 -1.00 )
+DEAL::1: ( 0.707 -0.707 )
+DEAL::2: ( 0 -0.646 )
+DEAL::3: ( 0.500 -0.500 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.500 -0.500 )
+DEAL::1: ( 0 -0.646 )
+DEAL::2: ( -0.293 -0.293 )
+DEAL::3: ( 0 -0.293 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 -0.646 )
+DEAL::1: ( 0.500 -0.500 )
+DEAL::2: ( 0 -0.293 )
+DEAL::3: ( 0.293 -0.293 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.707 -0.707 )
+DEAL::1: ( -0.500 -0.500 )
+DEAL::2: ( -1.00 0 )
+DEAL::3: ( -0.646 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.500 -0.500 )
+DEAL::1: ( -0.293 -0.293 )
+DEAL::2: ( -0.646 0 )
+DEAL::3: ( -0.293 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -1.00 0 )
+DEAL::1: ( -0.646 0 )
+DEAL::2: ( -0.707 0.707 )
+DEAL::3: ( -0.500 0.500 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.646 0 )
+DEAL::1: ( -0.293 0 )
+DEAL::2: ( -0.500 0.500 )
+DEAL::3: ( -0.293 0.293 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.293 -0.293 )
+DEAL::1: ( 0 -0.293 )
+DEAL::2: ( -0.293 0 )
+DEAL::3: ( 0 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 -0.293 )
+DEAL::1: ( 0.293 -0.293 )
+DEAL::2: ( 0 0 )
+DEAL::3: ( 0.293 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.293 0 )
+DEAL::1: ( 0 0 )
+DEAL::2: ( -0.293 0.293 )
+DEAL::3: ( 0 0.293 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 0 )
+DEAL::1: ( 0.293 0 )
+DEAL::2: ( 0 0.293 )
+DEAL::3: ( 0.293 0.293 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.707 -0.707 )
+DEAL::1: ( 1.00 0 )
+DEAL::2: ( 0.500 -0.500 )
+DEAL::3: ( 0.646 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 1.00 0 )
+DEAL::1: ( 0.707 0.707 )
+DEAL::2: ( 0.646 0 )
+DEAL::3: ( 0.500 0.500 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.500 -0.500 )
+DEAL::1: ( 0.646 0 )
+DEAL::2: ( 0.293 -0.293 )
+DEAL::3: ( 0.293 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.646 0 )
+DEAL::1: ( 0.500 0.500 )
+DEAL::2: ( 0.293 0 )
+DEAL::3: ( 0.293 0.293 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.707 0.707 )
+DEAL::1: ( -0.500 0.500 )
+DEAL::2: ( 0 1.00 )
+DEAL::3: ( 0 0.646 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.500 0.500 )
+DEAL::1: ( -0.293 0.293 )
+DEAL::2: ( 0 0.646 )
+DEAL::3: ( 0 0.293 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 1.00 )
+DEAL::1: ( 0 0.646 )
+DEAL::2: ( 0.707 0.707 )
+DEAL::3: ( 0.500 0.500 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 0.646 )
+DEAL::1: ( 0 0.293 )
+DEAL::2: ( 0.500 0.500 )
+DEAL::3: ( 0.293 0.293 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::FE=FESystem<3>[FE_Q<3>(2)]
+DEAL::Cell nodes:
+DEAL::0: ( -0.211 -0.211 -0.211 )
+DEAL::1: ( 0 -0.211 -0.211 )
+DEAL::2: ( -0.211 0 -0.211 )
+DEAL::3: ( 0 0 -0.211 )
+DEAL::4: ( -0.211 -0.211 0 )
+DEAL::5: ( 0 -0.211 0 )
+DEAL::6: ( -0.211 0 0 )
+DEAL::7: ( 0 0 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 -0.211 -0.211 )
+DEAL::1: ( 0.211 -0.211 -0.211 )
+DEAL::2: ( 0 0 -0.211 )
+DEAL::3: ( 0.211 0 -0.211 )
+DEAL::4: ( 0 -0.211 0 )
+DEAL::5: ( 0.211 -0.211 0 )
+DEAL::6: ( 0 0 0 )
+DEAL::7: ( 0.211 0 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.211 0 -0.211 )
+DEAL::1: ( 0 0 -0.211 )
+DEAL::2: ( -0.211 0.211 -0.211 )
+DEAL::3: ( 0 0.211 -0.211 )
+DEAL::4: ( -0.211 0 0 )
+DEAL::5: ( 0 0 0 )
+DEAL::6: ( -0.211 0.211 0 )
+DEAL::7: ( 0 0.211 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 0 -0.211 )
+DEAL::1: ( 0.211 0 -0.211 )
+DEAL::2: ( 0 0.211 -0.211 )
+DEAL::3: ( 0.211 0.211 -0.211 )
+DEAL::4: ( 0 0 0 )
+DEAL::5: ( 0.211 0 0 )
+DEAL::6: ( 0 0.211 0 )
+DEAL::7: ( 0.211 0.211 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.211 -0.211 0 )
+DEAL::1: ( 0 -0.211 0 )
+DEAL::2: ( -0.211 0 0 )
+DEAL::3: ( 0 0 0 )
+DEAL::4: ( -0.211 -0.211 0.211 )
+DEAL::5: ( 0 -0.211 0.211 )
+DEAL::6: ( -0.211 0 0.211 )
+DEAL::7: ( 0 0 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 -0.211 0 )
+DEAL::1: ( 0.211 -0.211 0 )
+DEAL::2: ( 0 0 0 )
+DEAL::3: ( 0.211 0 0 )
+DEAL::4: ( 0 -0.211 0.211 )
+DEAL::5: ( 0.211 -0.211 0.211 )
+DEAL::6: ( 0 0 0.211 )
+DEAL::7: ( 0.211 0 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.211 0 0 )
+DEAL::1: ( 0 0 0 )
+DEAL::2: ( -0.211 0.211 0 )
+DEAL::3: ( 0 0.211 0 )
+DEAL::4: ( -0.211 0 0.211 )
+DEAL::5: ( 0 0 0.211 )
+DEAL::6: ( -0.211 0.211 0.211 )
+DEAL::7: ( 0 0.211 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 0 0 )
+DEAL::1: ( 0.211 0 0 )
+DEAL::2: ( 0 0.211 0 )
+DEAL::3: ( 0.211 0.211 0 )
+DEAL::4: ( 0 0 0.211 )
+DEAL::5: ( 0.211 0 0.211 )
+DEAL::6: ( 0 0.211 0.211 )
+DEAL::7: ( 0.211 0.211 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.577 -0.577 -0.577 )
+DEAL::1: ( 0 -0.707 -0.707 )
+DEAL::2: ( -0.707 0 -0.707 )
+DEAL::3: ( 0 0 -1.00 )
+DEAL::4: ( -0.394 -0.394 -0.394 )
+DEAL::5: ( 0 -0.419 -0.419 )
+DEAL::6: ( -0.419 0 -0.419 )
+DEAL::7: ( 0 0 -0.457 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 -0.707 -0.707 )
+DEAL::1: ( 0.577 -0.577 -0.577 )
+DEAL::2: ( 0 0 -1.00 )
+DEAL::3: ( 0.707 0 -0.707 )
+DEAL::4: ( 0 -0.419 -0.419 )
+DEAL::5: ( 0.394 -0.394 -0.394 )
+DEAL::6: ( 0 0 -0.457 )
+DEAL::7: ( 0.419 0 -0.419 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.707 0 -0.707 )
+DEAL::1: ( 0 0 -1.00 )
+DEAL::2: ( -0.577 0.577 -0.577 )
+DEAL::3: ( 0 0.707 -0.707 )
+DEAL::4: ( -0.419 0 -0.419 )
+DEAL::5: ( 0 0 -0.457 )
+DEAL::6: ( -0.394 0.394 -0.394 )
+DEAL::7: ( 0 0.419 -0.419 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 0 -1.00 )
+DEAL::1: ( 0.707 0 -0.707 )
+DEAL::2: ( 0 0.707 -0.707 )
+DEAL::3: ( 0.577 0.577 -0.577 )
+DEAL::4: ( 0 0 -0.457 )
+DEAL::5: ( 0.419 0 -0.419 )
+DEAL::6: ( 0 0.419 -0.419 )
+DEAL::7: ( 0.394 0.394 -0.394 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.394 -0.394 -0.394 )
+DEAL::1: ( 0 -0.419 -0.419 )
+DEAL::2: ( -0.419 0 -0.419 )
+DEAL::3: ( 0 0 -0.457 )
+DEAL::4: ( -0.211 -0.211 -0.211 )
+DEAL::5: ( 0 -0.211 -0.211 )
+DEAL::6: ( -0.211 0 -0.211 )
+DEAL::7: ( 0 0 -0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 -0.419 -0.419 )
+DEAL::1: ( 0.394 -0.394 -0.394 )
+DEAL::2: ( 0 0 -0.457 )
+DEAL::3: ( 0.419 0 -0.419 )
+DEAL::4: ( 0 -0.211 -0.211 )
+DEAL::5: ( 0.211 -0.211 -0.211 )
+DEAL::6: ( 0 0 -0.211 )
+DEAL::7: ( 0.211 0 -0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.419 0 -0.419 )
+DEAL::1: ( 0 0 -0.457 )
+DEAL::2: ( -0.394 0.394 -0.394 )
+DEAL::3: ( 0 0.419 -0.419 )
+DEAL::4: ( -0.211 0 -0.211 )
+DEAL::5: ( 0 0 -0.211 )
+DEAL::6: ( -0.211 0.211 -0.211 )
+DEAL::7: ( 0 0.211 -0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 0 -0.457 )
+DEAL::1: ( 0.419 0 -0.419 )
+DEAL::2: ( 0 0.419 -0.419 )
+DEAL::3: ( 0.394 0.394 -0.394 )
+DEAL::4: ( 0 0 -0.211 )
+DEAL::5: ( 0.211 0 -0.211 )
+DEAL::6: ( 0 0.211 -0.211 )
+DEAL::7: ( 0.211 0.211 -0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.577 -0.577 -0.577 )
+DEAL::1: ( 0.707 0 -0.707 )
+DEAL::2: ( 0.394 -0.394 -0.394 )
+DEAL::3: ( 0.419 0 -0.419 )
+DEAL::4: ( 0.707 -0.707 0 )
+DEAL::5: ( 1.00 0 0 )
+DEAL::6: ( 0.419 -0.419 0 )
+DEAL::7: ( 0.457 0 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.707 0 -0.707 )
+DEAL::1: ( 0.577 0.577 -0.577 )
+DEAL::2: ( 0.419 0 -0.419 )
+DEAL::3: ( 0.394 0.394 -0.394 )
+DEAL::4: ( 1.00 0 0 )
+DEAL::5: ( 0.707 0.707 0 )
+DEAL::6: ( 0.457 0 0 )
+DEAL::7: ( 0.419 0.419 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.394 -0.394 -0.394 )
+DEAL::1: ( 0.419 0 -0.419 )
+DEAL::2: ( 0.211 -0.211 -0.211 )
+DEAL::3: ( 0.211 0 -0.211 )
+DEAL::4: ( 0.419 -0.419 0 )
+DEAL::5: ( 0.457 0 0 )
+DEAL::6: ( 0.211 -0.211 0 )
+DEAL::7: ( 0.211 0 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.419 0 -0.419 )
+DEAL::1: ( 0.394 0.394 -0.394 )
+DEAL::2: ( 0.211 0 -0.211 )
+DEAL::3: ( 0.211 0.211 -0.211 )
+DEAL::4: ( 0.457 0 0 )
+DEAL::5: ( 0.419 0.419 0 )
+DEAL::6: ( 0.211 0 0 )
+DEAL::7: ( 0.211 0.211 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.707 -0.707 0 )
+DEAL::1: ( 1.00 0 0 )
+DEAL::2: ( 0.419 -0.419 0 )
+DEAL::3: ( 0.457 0 0 )
+DEAL::4: ( 0.577 -0.577 0.577 )
+DEAL::5: ( 0.707 0 0.707 )
+DEAL::6: ( 0.394 -0.394 0.394 )
+DEAL::7: ( 0.419 0 0.419 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 1.00 0 0 )
+DEAL::1: ( 0.707 0.707 0 )
+DEAL::2: ( 0.457 0 0 )
+DEAL::3: ( 0.419 0.419 0 )
+DEAL::4: ( 0.707 0 0.707 )
+DEAL::5: ( 0.577 0.577 0.577 )
+DEAL::6: ( 0.419 0 0.419 )
+DEAL::7: ( 0.394 0.394 0.394 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.419 -0.419 0 )
+DEAL::1: ( 0.457 0 0 )
+DEAL::2: ( 0.211 -0.211 0 )
+DEAL::3: ( 0.211 0 0 )
+DEAL::4: ( 0.394 -0.394 0.394 )
+DEAL::5: ( 0.419 0 0.419 )
+DEAL::6: ( 0.211 -0.211 0.211 )
+DEAL::7: ( 0.211 0 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0.457 0 0 )
+DEAL::1: ( 0.419 0.419 0 )
+DEAL::2: ( 0.211 0 0 )
+DEAL::3: ( 0.211 0.211 0 )
+DEAL::4: ( 0.419 0 0.419 )
+DEAL::5: ( 0.394 0.394 0.394 )
+DEAL::6: ( 0.211 0 0.211 )
+DEAL::7: ( 0.211 0.211 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.577 -0.577 0.577 )
+DEAL::1: ( 0 -0.707 0.707 )
+DEAL::2: ( -0.394 -0.394 0.394 )
+DEAL::3: ( 0 -0.419 0.419 )
+DEAL::4: ( -0.707 0 0.707 )
+DEAL::5: ( 0 0 1.00 )
+DEAL::6: ( -0.419 0 0.419 )
+DEAL::7: ( 0 0 0.457 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 -0.707 0.707 )
+DEAL::1: ( 0.577 -0.577 0.577 )
+DEAL::2: ( 0 -0.419 0.419 )
+DEAL::3: ( 0.394 -0.394 0.394 )
+DEAL::4: ( 0 0 1.00 )
+DEAL::5: ( 0.707 0 0.707 )
+DEAL::6: ( 0 0 0.457 )
+DEAL::7: ( 0.419 0 0.419 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.394 -0.394 0.394 )
+DEAL::1: ( 0 -0.419 0.419 )
+DEAL::2: ( -0.211 -0.211 0.211 )
+DEAL::3: ( 0 -0.211 0.211 )
+DEAL::4: ( -0.419 0 0.419 )
+DEAL::5: ( 0 0 0.457 )
+DEAL::6: ( -0.211 0 0.211 )
+DEAL::7: ( 0 0 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 -0.419 0.419 )
+DEAL::1: ( 0.394 -0.394 0.394 )
+DEAL::2: ( 0 -0.211 0.211 )
+DEAL::3: ( 0.211 -0.211 0.211 )
+DEAL::4: ( 0 0 0.457 )
+DEAL::5: ( 0.419 0 0.419 )
+DEAL::6: ( 0 0 0.211 )
+DEAL::7: ( 0.211 0 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.707 0 0.707 )
+DEAL::1: ( 0 0 1.00 )
+DEAL::2: ( -0.419 0 0.419 )
+DEAL::3: ( 0 0 0.457 )
+DEAL::4: ( -0.577 0.577 0.577 )
+DEAL::5: ( 0 0.707 0.707 )
+DEAL::6: ( -0.394 0.394 0.394 )
+DEAL::7: ( 0 0.419 0.419 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 0 1.00 )
+DEAL::1: ( 0.707 0 0.707 )
+DEAL::2: ( 0 0 0.457 )
+DEAL::3: ( 0.419 0 0.419 )
+DEAL::4: ( 0 0.707 0.707 )
+DEAL::5: ( 0.577 0.577 0.577 )
+DEAL::6: ( 0 0.419 0.419 )
+DEAL::7: ( 0.394 0.394 0.394 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.419 0 0.419 )
+DEAL::1: ( 0 0 0.457 )
+DEAL::2: ( -0.211 0 0.211 )
+DEAL::3: ( 0 0 0.211 )
+DEAL::4: ( -0.394 0.394 0.394 )
+DEAL::5: ( 0 0.419 0.419 )
+DEAL::6: ( -0.211 0.211 0.211 )
+DEAL::7: ( 0 0.211 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 0 0.457 )
+DEAL::1: ( 0.419 0 0.419 )
+DEAL::2: ( 0 0 0.211 )
+DEAL::3: ( 0.211 0 0.211 )
+DEAL::4: ( 0 0.419 0.419 )
+DEAL::5: ( 0.394 0.394 0.394 )
+DEAL::6: ( 0 0.211 0.211 )
+DEAL::7: ( 0.211 0.211 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.577 -0.577 -0.577 )
+DEAL::1: ( -0.394 -0.394 -0.394 )
+DEAL::2: ( -0.707 0 -0.707 )
+DEAL::3: ( -0.419 0 -0.419 )
+DEAL::4: ( -0.707 -0.707 0 )
+DEAL::5: ( -0.419 -0.419 0 )
+DEAL::6: ( -1.00 0 0 )
+DEAL::7: ( -0.457 0 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.394 -0.394 -0.394 )
+DEAL::1: ( -0.211 -0.211 -0.211 )
+DEAL::2: ( -0.419 0 -0.419 )
+DEAL::3: ( -0.211 0 -0.211 )
+DEAL::4: ( -0.419 -0.419 0 )
+DEAL::5: ( -0.211 -0.211 0 )
+DEAL::6: ( -0.457 0 0 )
+DEAL::7: ( -0.211 0 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.707 0 -0.707 )
+DEAL::1: ( -0.419 0 -0.419 )
+DEAL::2: ( -0.577 0.577 -0.577 )
+DEAL::3: ( -0.394 0.394 -0.394 )
+DEAL::4: ( -1.00 0 0 )
+DEAL::5: ( -0.457 0 0 )
+DEAL::6: ( -0.707 0.707 0 )
+DEAL::7: ( -0.419 0.419 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.419 0 -0.419 )
+DEAL::1: ( -0.211 0 -0.211 )
+DEAL::2: ( -0.394 0.394 -0.394 )
+DEAL::3: ( -0.211 0.211 -0.211 )
+DEAL::4: ( -0.457 0 0 )
+DEAL::5: ( -0.211 0 0 )
+DEAL::6: ( -0.419 0.419 0 )
+DEAL::7: ( -0.211 0.211 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.707 -0.707 0 )
+DEAL::1: ( -0.419 -0.419 0 )
+DEAL::2: ( -1.00 0 0 )
+DEAL::3: ( -0.457 0 0 )
+DEAL::4: ( -0.577 -0.577 0.577 )
+DEAL::5: ( -0.394 -0.394 0.394 )
+DEAL::6: ( -0.707 0 0.707 )
+DEAL::7: ( -0.419 0 0.419 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.419 -0.419 0 )
+DEAL::1: ( -0.211 -0.211 0 )
+DEAL::2: ( -0.457 0 0 )
+DEAL::3: ( -0.211 0 0 )
+DEAL::4: ( -0.394 -0.394 0.394 )
+DEAL::5: ( -0.211 -0.211 0.211 )
+DEAL::6: ( -0.419 0 0.419 )
+DEAL::7: ( -0.211 0 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -1.00 0 0 )
+DEAL::1: ( -0.457 0 0 )
+DEAL::2: ( -0.707 0.707 0 )
+DEAL::3: ( -0.419 0.419 0 )
+DEAL::4: ( -0.707 0 0.707 )
+DEAL::5: ( -0.419 0 0.419 )
+DEAL::6: ( -0.577 0.577 0.577 )
+DEAL::7: ( -0.394 0.394 0.394 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.457 0 0 )
+DEAL::1: ( -0.211 0 0 )
+DEAL::2: ( -0.419 0.419 0 )
+DEAL::3: ( -0.211 0.211 0 )
+DEAL::4: ( -0.419 0 0.419 )
+DEAL::5: ( -0.211 0 0.211 )
+DEAL::6: ( -0.394 0.394 0.394 )
+DEAL::7: ( -0.211 0.211 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.577 -0.577 -0.577 )
+DEAL::1: ( 0 -0.707 -0.707 )
+DEAL::2: ( -0.394 -0.394 -0.394 )
+DEAL::3: ( 0 -0.419 -0.419 )
+DEAL::4: ( -0.707 -0.707 0 )
+DEAL::5: ( 0 -1.00 0 )
+DEAL::6: ( -0.419 -0.419 0 )
+DEAL::7: ( 0 -0.457 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 -0.707 -0.707 )
+DEAL::1: ( 0.577 -0.577 -0.577 )
+DEAL::2: ( 0 -0.419 -0.419 )
+DEAL::3: ( 0.394 -0.394 -0.394 )
+DEAL::4: ( 0 -1.00 0 )
+DEAL::5: ( 0.707 -0.707 0 )
+DEAL::6: ( 0 -0.457 0 )
+DEAL::7: ( 0.419 -0.419 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.394 -0.394 -0.394 )
+DEAL::1: ( 0 -0.419 -0.419 )
+DEAL::2: ( -0.211 -0.211 -0.211 )
+DEAL::3: ( 0 -0.211 -0.211 )
+DEAL::4: ( -0.419 -0.419 0 )
+DEAL::5: ( 0 -0.457 0 )
+DEAL::6: ( -0.211 -0.211 0 )
+DEAL::7: ( 0 -0.211 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 -0.419 -0.419 )
+DEAL::1: ( 0.394 -0.394 -0.394 )
+DEAL::2: ( 0 -0.211 -0.211 )
+DEAL::3: ( 0.211 -0.211 -0.211 )
+DEAL::4: ( 0 -0.457 0 )
+DEAL::5: ( 0.419 -0.419 0 )
+DEAL::6: ( 0 -0.211 0 )
+DEAL::7: ( 0.211 -0.211 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.707 -0.707 0 )
+DEAL::1: ( 0 -1.00 0 )
+DEAL::2: ( -0.419 -0.419 0 )
+DEAL::3: ( 0 -0.457 0 )
+DEAL::4: ( -0.577 -0.577 0.577 )
+DEAL::5: ( 0 -0.707 0.707 )
+DEAL::6: ( -0.394 -0.394 0.394 )
+DEAL::7: ( 0 -0.419 0.419 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 -1.00 0 )
+DEAL::1: ( 0.707 -0.707 0 )
+DEAL::2: ( 0 -0.457 0 )
+DEAL::3: ( 0.419 -0.419 0 )
+DEAL::4: ( 0 -0.707 0.707 )
+DEAL::5: ( 0.577 -0.577 0.577 )
+DEAL::6: ( 0 -0.419 0.419 )
+DEAL::7: ( 0.394 -0.394 0.394 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.419 -0.419 0 )
+DEAL::1: ( 0 -0.457 0 )
+DEAL::2: ( -0.211 -0.211 0 )
+DEAL::3: ( 0 -0.211 0 )
+DEAL::4: ( -0.394 -0.394 0.394 )
+DEAL::5: ( 0 -0.419 0.419 )
+DEAL::6: ( -0.211 -0.211 0.211 )
+DEAL::7: ( 0 -0.211 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 -0.457 0 )
+DEAL::1: ( 0.419 -0.419 0 )
+DEAL::2: ( 0 -0.211 0 )
+DEAL::3: ( 0.211 -0.211 0 )
+DEAL::4: ( 0 -0.419 0.419 )
+DEAL::5: ( 0.394 -0.394 0.394 )
+DEAL::6: ( 0 -0.211 0.211 )
+DEAL::7: ( 0.211 -0.211 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.577 0.577 -0.577 )
+DEAL::1: ( -0.394 0.394 -0.394 )
+DEAL::2: ( 0 0.707 -0.707 )
+DEAL::3: ( 0 0.419 -0.419 )
+DEAL::4: ( -0.707 0.707 0 )
+DEAL::5: ( -0.419 0.419 0 )
+DEAL::6: ( 0 1.00 0 )
+DEAL::7: ( 0 0.457 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.394 0.394 -0.394 )
+DEAL::1: ( -0.211 0.211 -0.211 )
+DEAL::2: ( 0 0.419 -0.419 )
+DEAL::3: ( 0 0.211 -0.211 )
+DEAL::4: ( -0.419 0.419 0 )
+DEAL::5: ( -0.211 0.211 0 )
+DEAL::6: ( 0 0.457 0 )
+DEAL::7: ( 0 0.211 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 0.707 -0.707 )
+DEAL::1: ( 0 0.419 -0.419 )
+DEAL::2: ( 0.577 0.577 -0.577 )
+DEAL::3: ( 0.394 0.394 -0.394 )
+DEAL::4: ( 0 1.00 0 )
+DEAL::5: ( 0 0.457 0 )
+DEAL::6: ( 0.707 0.707 0 )
+DEAL::7: ( 0.419 0.419 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 0.419 -0.419 )
+DEAL::1: ( 0 0.211 -0.211 )
+DEAL::2: ( 0.394 0.394 -0.394 )
+DEAL::3: ( 0.211 0.211 -0.211 )
+DEAL::4: ( 0 0.457 0 )
+DEAL::5: ( 0 0.211 0 )
+DEAL::6: ( 0.419 0.419 0 )
+DEAL::7: ( 0.211 0.211 0 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.707 0.707 0 )
+DEAL::1: ( -0.419 0.419 0 )
+DEAL::2: ( 0 1.00 0 )
+DEAL::3: ( 0 0.457 0 )
+DEAL::4: ( -0.577 0.577 0.577 )
+DEAL::5: ( -0.394 0.394 0.394 )
+DEAL::6: ( 0 0.707 0.707 )
+DEAL::7: ( 0 0.419 0.419 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( -0.419 0.419 0 )
+DEAL::1: ( -0.211 0.211 0 )
+DEAL::2: ( 0 0.457 0 )
+DEAL::3: ( 0 0.211 0 )
+DEAL::4: ( -0.394 0.394 0.394 )
+DEAL::5: ( -0.211 0.211 0.211 )
+DEAL::6: ( 0 0.419 0.419 )
+DEAL::7: ( 0 0.211 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 1.00 0 )
+DEAL::1: ( 0 0.457 0 )
+DEAL::2: ( 0.707 0.707 0 )
+DEAL::3: ( 0.419 0.419 0 )
+DEAL::4: ( 0 0.707 0.707 )
+DEAL::5: ( 0 0.419 0.419 )
+DEAL::6: ( 0.577 0.577 0.577 )
+DEAL::7: ( 0.394 0.394 0.394 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::Cell nodes:
+DEAL::0: ( 0 0.457 0 )
+DEAL::1: ( 0 0.211 0 )
+DEAL::2: ( 0.419 0.419 0 )
+DEAL::3: ( 0.211 0.211 0 )
+DEAL::4: ( 0 0.419 0.419 )
+DEAL::5: ( 0 0.211 0.211 )
+DEAL::6: ( 0.394 0.394 0.394 )
+DEAL::7: ( 0.211 0.211 0.211 )
+DEAL::OK: cell bulk and boundary integrals match...
+
+DEAL::done...