Add test of functionality

diff --git a/include/deal.II/numerics/vector_tools.templates.h b/include/deal.II/numerics/vector_tools.templates.h
index ab6c5ff0090be2ab423126447c6088badd786d62..cc8987ebc6a9e053f22e0a46d3ec87ce75848de3 100644 (file)
--- a/include/deal.II/numerics/vector_tools.templates.h
+++ b/include/deal.II/numerics/vector_tools.templates.h
@@ -122,29 +122,21 @@ namespace VectorTools
           {
             if (component_mask[component_index] == true)
               {
-                std::pair<unsigned int, unsigned int> base_index = fe[fe_index].component_to_base_index(component_index);
-
-                AssertThrow ((fe[fe_index].base_element(base_index.first).has_support_points()) ||
-                             (fe[fe_index].base_element(base_index.first).dofs_per_cell == 0),
-                             ExcNonInterpolatingFE());
+                Assert ((fe[fe_index].base_element(fe[fe_index].component_to_base_index(component_index).first).has_support_points()) ||
+                        (fe[fe_index].base_element(fe[fe_index].component_to_base_index(component_index).first).dofs_per_cell == 0),
+                        ExcNonInterpolatingFE());
               }
           }
       }
 
-    // Find the support points on a cell that
-    // are mentioned multiple times, and ony add
-    // each once.
-    // Each multiple point gets to know the dof
-    // index of its representative point by the
-    // dof_to_rep_dof_table.
+    // Find the support points on a cell that are mentioned multiple times, and
+    // only add each once.  Each multiple point gets to know the dof index of
+    // its representative point by the dof_to_rep_dof_table.
 
     // the following vector collects all unit support points p[i],
-    // 0<=i<fe.dofs_per_cell, for that
-    // unit_support_point(i)
-    // is a representative one. i.e.
-    // the following vector collects all rep dofs.
-    // the position of a rep dof within this vector
-    // is called rep index.
+    // 0<=i<fe.dofs_per_cell, for which unit_support_point(i) is unique
+    // (representative). The position of a support point within this vector is
+    // called the rep index.
     std::vector<std::vector<Point<dim> > > rep_unit_support_points (fe.size());
     // the following table converts a dof i
     // to the rep index.
@@ -160,7 +152,7 @@ namespace VectorTools
               = fe[fe_index].system_to_component_index(i).first;
             if (component_mask[component] == true)
               {
-                Point<dim> dof_support_point = fe[fe_index].unit_support_point(i);
+                const Point<dim> dof_support_point = fe[fe_index].unit_support_point(i);
 
                 bool representative=true;
                 // the following loop is looped

diff --git a/tests/dofs/interpolate_q_system_mixed_01.cc b/tests/dofs/interpolate_q_system_mixed_01.cc
new file mode 100644 (file)
index 0000000..0b5570c
--- /dev/null
+++ b/tests/dofs/interpolate_q_system_mixed_01.cc
@@ -0,0 +1,189 @@
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2006 - 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 that VectorTools::interpolate with a component mask works for
+// FE_System(FE_Q(p)) elements correctly on a uniformly refined mesh for
+// functions of degree q when a non-interpolating (FE_DGP(p)) element is also
+// included in the system.
+
+#include "../tests.h"
+#include <deal.II/base/function.h>
+#include <deal.II/base/logstream.h>
+#include <deal.II/base/quadrature_lib.h>
+#include <deal.II/lac/vector.h>
+
+#include <deal.II/grid/tria.h>
+#include <deal.II/dofs/dof_handler.h>
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/grid_refinement.h>
+#include <deal.II/grid/tria_accessor.h>
+#include <deal.II/grid/tria_iterator.h>
+#include <deal.II/grid/tria_boundary_lib.h>
+#include <deal.II/dofs/dof_accessor.h>
+#include <deal.II/dofs/dof_tools.h>
+#include <deal.II/numerics/vector_tools.h>
+#include <deal.II/fe/fe_q.h>
+#include <deal.II/fe/fe_dgp.h>
+#include <deal.II/fe/fe_system.h>
+
+#include <fstream>
+#include <vector>
+
+
+template <int dim>
+class F :  public Function<dim>
+{
+public:
+  F (const unsigned int q, const double adj) : Function<dim>(4), q(q), adj(adj) {}
+
+  virtual void vector_value (const Point<dim> &p,
+                             Vector<double>   &v) const
+  {
+    for (unsigned int c=0; c<v.size(); ++c)
+      {
+        v(c) = 0;
+        for (unsigned int d=0; d<dim; ++d)
+          for (unsigned int i=0; i<=q; ++i)
+            v(c) += (d+1)*(i+1)*std::pow (p[d], 1.*i)+c+adj;
+      }
+  }
+
+private:
+  const unsigned int q;
+  const double adj;
+};
+
+
+
+template <int dim>
+void test ()
+{
+  Triangulation<dim>     triangulation;
+  GridGenerator::hyper_cube (triangulation);
+  triangulation.refine_global (3);
+
+  for (unsigned int p=1; p<6-dim; ++p)
+    {
+      FE_Q<dim> fe_1(p);
+      FE_Q<dim> fe_2(p+1);
+      FE_DGP<dim> fe_3(p);
+      FESystem<dim>              fe(fe_1, 2,
+                                    fe_2, 1,
+                                    fe_3, 1);
+      DoFHandler<dim>        dof_handler(triangulation);
+      dof_handler.distribute_dofs (fe);
+
+      // Use constant offset to distinguish between masks
+      const double adj1 = 0.3;
+      ComponentSelectFunction<dim> select_mask1(0,4);
+      ComponentMask mask1(4, false);
+      mask1.set(0, true);
+
+      const double adj2 = 1.7;
+      ComponentSelectFunction<dim> select_mask2(std::make_pair(1,3),4);
+      ComponentMask mask2(4, false);
+      mask2.set(1, true);
+      mask2.set(2, true);
+
+      ComponentMask mask_fail(4, false);
+      mask_fail.set(3, true);
+
+      Vector<double> interpolant (dof_handler.n_dofs());
+      Vector<float>  error (triangulation.n_active_cells());
+      for (unsigned int q=0; q<=p+2; ++q)
+        {
+          // interpolate the function with mask 1
+          VectorTools::interpolate (dof_handler,
+                                    F<dim> (q, adj1),
+                                    interpolant,
+                                    mask1);
+
+          // interpolate the function with mask 2
+          VectorTools::interpolate (dof_handler,
+                                    F<dim> (q, adj2),
+                                    interpolant,
+                                    mask2);
+
+          // then compute the interpolation error for mask 1
+          VectorTools::integrate_difference (dof_handler,
+                                             interpolant,
+                                             F<dim> (q, adj1),
+                                             error,
+                                             QGauss<dim>(q+2),
+                                             VectorTools::L2_norm,
+                                             &select_mask1);
+          if (q<=p)
+            Assert (error.l2_norm() < 1e-12*interpolant.l2_norm(),
+                    ExcInternalError());
+
+          deallog << fe.get_name() << ", Mask 1, P_" << q
+                  << ", rel. error=" << error.l2_norm() / interpolant.l2_norm()
+                  << std::endl;
+
+          // then compute the interpolation error for mask 2
+          VectorTools::integrate_difference (dof_handler,
+                                             interpolant,
+                                             F<dim> (q, adj2),
+                                             error,
+                                             QGauss<dim>(q+2),
+                                             VectorTools::L2_norm,
+                                             &select_mask2);
+          if (q<=p)
+            Assert (error.l2_norm() < 1e-12*interpolant.l2_norm(),
+                    ExcInternalError());
+
+          deallog << fe.get_name() << ", Mask 2, P_" << q
+                  << ", rel. error=" << error.l2_norm() / interpolant.l2_norm()
+                  << std::endl;
+        }
+
+      // Test for correct failure
+      deallog << fe.get_name()
+              << ", Fails for including non-interpolating FE ";
+      try
+        {
+          VectorTools::interpolate (dof_handler,
+                                    F<dim> (0, 0.0),
+                                    interpolant,
+                                    mask_fail);
+        }
+      catch (const ExceptionBase &e)
+        {
+          deallog << "OK" << std::endl;
+          deallog << "\tFails with " << e.get_exc_name() << std::endl;
+        }
+      deallog << std::endl;
+    }
+}
+
+
+
+int main ()
+{
+  deal_II_exceptions::disable_abort_on_exception();
+
+  std::ofstream logfile("output");
+  deallog << std::setprecision (3);
+
+  deallog.attach(logfile);
+  deallog.threshold_double(1.e-10);
+
+  test<1>();
+  test<2>();
+  test<3>();
+}
+

diff --git a/tests/dofs/interpolate_q_system_mixed_01.debug.output b/tests/dofs/interpolate_q_system_mixed_01.debug.output
new file mode 100644 (file)
index 0000000..a8843b6
--- /dev/null
+++ b/tests/dofs/interpolate_q_system_mixed_01.debug.output
@@ -0,0 +1,120 @@
+
+DEAL::FESystem<1>[FE_Q<1>(1)^2-FE_Q<1>(2)-FE_DGP<1>(1)], Mask 1, P_0, rel. error=0
+DEAL::FESystem<1>[FE_Q<1>(1)^2-FE_Q<1>(2)-FE_DGP<1>(1)], Mask 2, P_0, rel. error=0
+DEAL::FESystem<1>[FE_Q<1>(1)^2-FE_Q<1>(2)-FE_DGP<1>(1)], Mask 1, P_1, rel. error=0
+DEAL::FESystem<1>[FE_Q<1>(1)^2-FE_Q<1>(2)-FE_DGP<1>(1)], Mask 2, P_1, rel. error=0
+DEAL::FESystem<1>[FE_Q<1>(1)^2-FE_Q<1>(2)-FE_DGP<1>(1)], Mask 1, P_2, rel. error=0.000124
+DEAL::FESystem<1>[FE_Q<1>(1)^2-FE_Q<1>(2)-FE_DGP<1>(1)], Mask 2, P_2, rel. error=0.000124
+DEAL::FESystem<1>[FE_Q<1>(1)^2-FE_Q<1>(2)-FE_DGP<1>(1)], Mask 1, P_3, rel. error=0.000296
+DEAL::FESystem<1>[FE_Q<1>(1)^2-FE_Q<1>(2)-FE_DGP<1>(1)], Mask 2, P_3, rel. error=0.000296
+DEAL::FESystem<1>[FE_Q<1>(1)^2-FE_Q<1>(2)-FE_DGP<1>(1)], Fails for including non-interpolating FE OK
+DEAL:: Fails with ExcNonInterpolatingFE()
+DEAL::
+DEAL::FESystem<1>[FE_Q<1>(2)^2-FE_Q<1>(3)-FE_DGP<1>(2)], Mask 1, P_0, rel. error=0
+DEAL::FESystem<1>[FE_Q<1>(2)^2-FE_Q<1>(3)-FE_DGP<1>(2)], Mask 2, P_0, rel. error=0
+DEAL::FESystem<1>[FE_Q<1>(2)^2-FE_Q<1>(3)-FE_DGP<1>(2)], Mask 1, P_1, rel. error=0
+DEAL::FESystem<1>[FE_Q<1>(2)^2-FE_Q<1>(3)-FE_DGP<1>(2)], Mask 2, P_1, rel. error=0
+DEAL::FESystem<1>[FE_Q<1>(2)^2-FE_Q<1>(3)-FE_DGP<1>(2)], Mask 1, P_2, rel. error=0
+DEAL::FESystem<1>[FE_Q<1>(2)^2-FE_Q<1>(3)-FE_DGP<1>(2)], Mask 2, P_2, rel. error=0
+DEAL::FESystem<1>[FE_Q<1>(2)^2-FE_Q<1>(3)-FE_DGP<1>(2)], Mask 1, P_3, rel. error=2.31e-06
+DEAL::FESystem<1>[FE_Q<1>(2)^2-FE_Q<1>(3)-FE_DGP<1>(2)], Mask 2, P_3, rel. error=2.31e-06
+DEAL::FESystem<1>[FE_Q<1>(2)^2-FE_Q<1>(3)-FE_DGP<1>(2)], Mask 1, P_4, rel. error=6.92e-06
+DEAL::FESystem<1>[FE_Q<1>(2)^2-FE_Q<1>(3)-FE_DGP<1>(2)], Mask 2, P_4, rel. error=6.92e-06
+DEAL::FESystem<1>[FE_Q<1>(2)^2-FE_Q<1>(3)-FE_DGP<1>(2)], Fails for including non-interpolating FE OK
+DEAL:: Fails with ExcNonInterpolatingFE()
+DEAL::
+DEAL::FESystem<1>[FE_Q<1>(3)^2-FE_Q<1>(4)-FE_DGP<1>(3)], Mask 1, P_0, rel. error=0
+DEAL::FESystem<1>[FE_Q<1>(3)^2-FE_Q<1>(4)-FE_DGP<1>(3)], Mask 2, P_0, rel. error=0
+DEAL::FESystem<1>[FE_Q<1>(3)^2-FE_Q<1>(4)-FE_DGP<1>(3)], Mask 1, P_1, rel. error=0
+DEAL::FESystem<1>[FE_Q<1>(3)^2-FE_Q<1>(4)-FE_DGP<1>(3)], Mask 2, P_1, rel. error=0
+DEAL::FESystem<1>[FE_Q<1>(3)^2-FE_Q<1>(4)-FE_DGP<1>(3)], Mask 1, P_2, rel. error=0
+DEAL::FESystem<1>[FE_Q<1>(3)^2-FE_Q<1>(4)-FE_DGP<1>(3)], Mask 2, P_2, rel. error=0
+DEAL::FESystem<1>[FE_Q<1>(3)^2-FE_Q<1>(4)-FE_DGP<1>(3)], Mask 1, P_3, rel. error=0
+DEAL::FESystem<1>[FE_Q<1>(3)^2-FE_Q<1>(4)-FE_DGP<1>(3)], Mask 2, P_3, rel. error=0
+DEAL::FESystem<1>[FE_Q<1>(3)^2-FE_Q<1>(4)-FE_DGP<1>(3)], Mask 1, P_4, rel. error=5.66e-08
+DEAL::FESystem<1>[FE_Q<1>(3)^2-FE_Q<1>(4)-FE_DGP<1>(3)], Mask 2, P_4, rel. error=5.66e-08
+DEAL::FESystem<1>[FE_Q<1>(3)^2-FE_Q<1>(4)-FE_DGP<1>(3)], Mask 1, P_5, rel. error=2.03e-07
+DEAL::FESystem<1>[FE_Q<1>(3)^2-FE_Q<1>(4)-FE_DGP<1>(3)], Mask 2, P_5, rel. error=2.03e-07
+DEAL::FESystem<1>[FE_Q<1>(3)^2-FE_Q<1>(4)-FE_DGP<1>(3)], Fails for including non-interpolating FE OK
+DEAL:: Fails with ExcNonInterpolatingFE()
+DEAL::
+DEAL::FESystem<1>[FE_Q<1>(4)^2-FE_Q<1>(5)-FE_DGP<1>(4)], Mask 1, P_0, rel. error=0
+DEAL::FESystem<1>[FE_Q<1>(4)^2-FE_Q<1>(5)-FE_DGP<1>(4)], Mask 2, P_0, rel. error=0
+DEAL::FESystem<1>[FE_Q<1>(4)^2-FE_Q<1>(5)-FE_DGP<1>(4)], Mask 1, P_1, rel. error=0
+DEAL::FESystem<1>[FE_Q<1>(4)^2-FE_Q<1>(5)-FE_DGP<1>(4)], Mask 2, P_1, rel. error=0
+DEAL::FESystem<1>[FE_Q<1>(4)^2-FE_Q<1>(5)-FE_DGP<1>(4)], Mask 1, P_2, rel. error=0
+DEAL::FESystem<1>[FE_Q<1>(4)^2-FE_Q<1>(5)-FE_DGP<1>(4)], Mask 2, P_2, rel. error=0
+DEAL::FESystem<1>[FE_Q<1>(4)^2-FE_Q<1>(5)-FE_DGP<1>(4)], Mask 1, P_3, rel. error=0
+DEAL::FESystem<1>[FE_Q<1>(4)^2-FE_Q<1>(5)-FE_DGP<1>(4)], Mask 2, P_3, rel. error=0
+DEAL::FESystem<1>[FE_Q<1>(4)^2-FE_Q<1>(5)-FE_DGP<1>(4)], Mask 1, P_4, rel. error=0
+DEAL::FESystem<1>[FE_Q<1>(4)^2-FE_Q<1>(5)-FE_DGP<1>(4)], Mask 2, P_4, rel. error=0
+DEAL::FESystem<1>[FE_Q<1>(4)^2-FE_Q<1>(5)-FE_DGP<1>(4)], Mask 1, P_5, rel. error=1.50e-09
+DEAL::FESystem<1>[FE_Q<1>(4)^2-FE_Q<1>(5)-FE_DGP<1>(4)], Mask 2, P_5, rel. error=1.50e-09
+DEAL::FESystem<1>[FE_Q<1>(4)^2-FE_Q<1>(5)-FE_DGP<1>(4)], Mask 1, P_6, rel. error=6.27e-09
+DEAL::FESystem<1>[FE_Q<1>(4)^2-FE_Q<1>(5)-FE_DGP<1>(4)], Mask 2, P_6, rel. error=6.27e-09
+DEAL::FESystem<1>[FE_Q<1>(4)^2-FE_Q<1>(5)-FE_DGP<1>(4)], Fails for including non-interpolating FE OK
+DEAL:: Fails with ExcNonInterpolatingFE()
+DEAL::
+DEAL::FESystem<2>[FE_Q<2>(1)^2-FE_Q<2>(2)-FE_DGP<2>(1)], Mask 1, P_0, rel. error=0
+DEAL::FESystem<2>[FE_Q<2>(1)^2-FE_Q<2>(2)-FE_DGP<2>(1)], Mask 2, P_0, rel. error=0
+DEAL::FESystem<2>[FE_Q<2>(1)^2-FE_Q<2>(2)-FE_DGP<2>(1)], Mask 1, P_1, rel. error=0
+DEAL::FESystem<2>[FE_Q<2>(1)^2-FE_Q<2>(2)-FE_DGP<2>(1)], Mask 2, P_1, rel. error=0
+DEAL::FESystem<2>[FE_Q<2>(1)^2-FE_Q<2>(2)-FE_DGP<2>(1)], Mask 1, P_2, rel. error=4.17e-05
+DEAL::FESystem<2>[FE_Q<2>(1)^2-FE_Q<2>(2)-FE_DGP<2>(1)], Mask 2, P_2, rel. error=4.17e-05
+DEAL::FESystem<2>[FE_Q<2>(1)^2-FE_Q<2>(2)-FE_DGP<2>(1)], Mask 1, P_3, rel. error=9.68e-05
+DEAL::FESystem<2>[FE_Q<2>(1)^2-FE_Q<2>(2)-FE_DGP<2>(1)], Mask 2, P_3, rel. error=9.68e-05
+DEAL::FESystem<2>[FE_Q<2>(1)^2-FE_Q<2>(2)-FE_DGP<2>(1)], Fails for including non-interpolating FE OK
+DEAL:: Fails with ExcNonInterpolatingFE()
+DEAL::
+DEAL::FESystem<2>[FE_Q<2>(2)^2-FE_Q<2>(3)-FE_DGP<2>(2)], Mask 1, P_0, rel. error=0
+DEAL::FESystem<2>[FE_Q<2>(2)^2-FE_Q<2>(3)-FE_DGP<2>(2)], Mask 2, P_0, rel. error=0
+DEAL::FESystem<2>[FE_Q<2>(2)^2-FE_Q<2>(3)-FE_DGP<2>(2)], Mask 1, P_1, rel. error=0
+DEAL::FESystem<2>[FE_Q<2>(2)^2-FE_Q<2>(3)-FE_DGP<2>(2)], Mask 2, P_1, rel. error=0
+DEAL::FESystem<2>[FE_Q<2>(2)^2-FE_Q<2>(3)-FE_DGP<2>(2)], Mask 1, P_2, rel. error=0
+DEAL::FESystem<2>[FE_Q<2>(2)^2-FE_Q<2>(3)-FE_DGP<2>(2)], Mask 2, P_2, rel. error=0
+DEAL::FESystem<2>[FE_Q<2>(2)^2-FE_Q<2>(3)-FE_DGP<2>(2)], Mask 1, P_3, rel. error=4.87e-07
+DEAL::FESystem<2>[FE_Q<2>(2)^2-FE_Q<2>(3)-FE_DGP<2>(2)], Mask 2, P_3, rel. error=4.87e-07
+DEAL::FESystem<2>[FE_Q<2>(2)^2-FE_Q<2>(3)-FE_DGP<2>(2)], Mask 1, P_4, rel. error=1.46e-06
+DEAL::FESystem<2>[FE_Q<2>(2)^2-FE_Q<2>(3)-FE_DGP<2>(2)], Mask 2, P_4, rel. error=1.46e-06
+DEAL::FESystem<2>[FE_Q<2>(2)^2-FE_Q<2>(3)-FE_DGP<2>(2)], Fails for including non-interpolating FE OK
+DEAL:: Fails with ExcNonInterpolatingFE()
+DEAL::
+DEAL::FESystem<2>[FE_Q<2>(3)^2-FE_Q<2>(4)-FE_DGP<2>(3)], Mask 1, P_0, rel. error=0
+DEAL::FESystem<2>[FE_Q<2>(3)^2-FE_Q<2>(4)-FE_DGP<2>(3)], Mask 2, P_0, rel. error=0
+DEAL::FESystem<2>[FE_Q<2>(3)^2-FE_Q<2>(4)-FE_DGP<2>(3)], Mask 1, P_1, rel. error=0
+DEAL::FESystem<2>[FE_Q<2>(3)^2-FE_Q<2>(4)-FE_DGP<2>(3)], Mask 2, P_1, rel. error=0
+DEAL::FESystem<2>[FE_Q<2>(3)^2-FE_Q<2>(4)-FE_DGP<2>(3)], Mask 1, P_2, rel. error=0
+DEAL::FESystem<2>[FE_Q<2>(3)^2-FE_Q<2>(4)-FE_DGP<2>(3)], Mask 2, P_2, rel. error=0
+DEAL::FESystem<2>[FE_Q<2>(3)^2-FE_Q<2>(4)-FE_DGP<2>(3)], Mask 1, P_3, rel. error=0
+DEAL::FESystem<2>[FE_Q<2>(3)^2-FE_Q<2>(4)-FE_DGP<2>(3)], Mask 2, P_3, rel. error=0
+DEAL::FESystem<2>[FE_Q<2>(3)^2-FE_Q<2>(4)-FE_DGP<2>(3)], Mask 1, P_4, rel. error=1.02e-08
+DEAL::FESystem<2>[FE_Q<2>(3)^2-FE_Q<2>(4)-FE_DGP<2>(3)], Mask 2, P_4, rel. error=1.02e-08
+DEAL::FESystem<2>[FE_Q<2>(3)^2-FE_Q<2>(4)-FE_DGP<2>(3)], Mask 1, P_5, rel. error=3.68e-08
+DEAL::FESystem<2>[FE_Q<2>(3)^2-FE_Q<2>(4)-FE_DGP<2>(3)], Mask 2, P_5, rel. error=3.68e-08
+DEAL::FESystem<2>[FE_Q<2>(3)^2-FE_Q<2>(4)-FE_DGP<2>(3)], Fails for including non-interpolating FE OK
+DEAL:: Fails with ExcNonInterpolatingFE()
+DEAL::
+DEAL::FESystem<3>[FE_Q<3>(1)^2-FE_Q<3>(2)-FE_DGP<3>(1)], Mask 1, P_0, rel. error=0
+DEAL::FESystem<3>[FE_Q<3>(1)^2-FE_Q<3>(2)-FE_DGP<3>(1)], Mask 2, P_0, rel. error=0
+DEAL::FESystem<3>[FE_Q<3>(1)^2-FE_Q<3>(2)-FE_DGP<3>(1)], Mask 1, P_1, rel. error=0
+DEAL::FESystem<3>[FE_Q<3>(1)^2-FE_Q<3>(2)-FE_DGP<3>(1)], Mask 2, P_1, rel. error=0
+DEAL::FESystem<3>[FE_Q<3>(1)^2-FE_Q<3>(2)-FE_DGP<3>(1)], Mask 1, P_2, rel. error=1.26e-05
+DEAL::FESystem<3>[FE_Q<3>(1)^2-FE_Q<3>(2)-FE_DGP<3>(1)], Mask 2, P_2, rel. error=1.26e-05
+DEAL::FESystem<3>[FE_Q<3>(1)^2-FE_Q<3>(2)-FE_DGP<3>(1)], Mask 1, P_3, rel. error=2.89e-05
+DEAL::FESystem<3>[FE_Q<3>(1)^2-FE_Q<3>(2)-FE_DGP<3>(1)], Mask 2, P_3, rel. error=2.89e-05
+DEAL::FESystem<3>[FE_Q<3>(1)^2-FE_Q<3>(2)-FE_DGP<3>(1)], Fails for including non-interpolating FE OK
+DEAL:: Fails with ExcNonInterpolatingFE()
+DEAL::
+DEAL::FESystem<3>[FE_Q<3>(2)^2-FE_Q<3>(3)-FE_DGP<3>(2)], Mask 1, P_0, rel. error=0
+DEAL::FESystem<3>[FE_Q<3>(2)^2-FE_Q<3>(3)-FE_DGP<3>(2)], Mask 2, P_0, rel. error=0
+DEAL::FESystem<3>[FE_Q<3>(2)^2-FE_Q<3>(3)-FE_DGP<3>(2)], Mask 1, P_1, rel. error=0
+DEAL::FESystem<3>[FE_Q<3>(2)^2-FE_Q<3>(3)-FE_DGP<3>(2)], Mask 2, P_1, rel. error=0
+DEAL::FESystem<3>[FE_Q<3>(2)^2-FE_Q<3>(3)-FE_DGP<3>(2)], Mask 1, P_2, rel. error=0
+DEAL::FESystem<3>[FE_Q<3>(2)^2-FE_Q<3>(3)-FE_DGP<3>(2)], Mask 2, P_2, rel. error=0
+DEAL::FESystem<3>[FE_Q<3>(2)^2-FE_Q<3>(3)-FE_DGP<3>(2)], Mask 1, P_3, rel. error=1.03e-07
+DEAL::FESystem<3>[FE_Q<3>(2)^2-FE_Q<3>(3)-FE_DGP<3>(2)], Mask 2, P_3, rel. error=1.03e-07
+DEAL::FESystem<3>[FE_Q<3>(2)^2-FE_Q<3>(3)-FE_DGP<3>(2)], Mask 1, P_4, rel. error=3.08e-07
+DEAL::FESystem<3>[FE_Q<3>(2)^2-FE_Q<3>(3)-FE_DGP<3>(2)], Mask 2, P_4, rel. error=3.08e-07
+DEAL::FESystem<3>[FE_Q<3>(2)^2-FE_Q<3>(3)-FE_DGP<3>(2)], Fails for including non-interpolating FE OK
+DEAL:: Fails with ExcNonInterpolatingFE()
+DEAL::