Add tests for the BR element.

diff --git a/tests/fe/br_approximation_01.cc b/tests/fe/br_approximation_01.cc
new file mode 100644 (file)
index 0000000..e8457e3
--- /dev/null
+++ b/tests/fe/br_approximation_01.cc
@@ -0,0 +1,518 @@
+// ---------------------------------------------------------------------
+//
+//
+//
+//
+//
+//
+//
+//
+//
+//
+//
+//
+// ---------------------------------------------------------------------
+
+
+// projects the shape functions from the Bernardi-Raugel elements
+// into different polynomial spaces and computes the error of the
+// approximation. The error should be close to machine precision
+// for polynomials of degree 2 or higher
+
+// this is almost a verbatim copy of rt_approximation_01.cc and
+// may needs additional modifications to make it more robust
+
+#include "../tests.h"
+
+#define PRECISION 8
+
+
+std::ofstream logfile("output");
+
+char buf[1000];
+
+
+#include <deal.II/base/function.h>
+#include <deal.II/base/quadrature_lib.h>
+
+#include <deal.II/dofs/dof_tools.h>
+
+#include <deal.II/fe/fe.h>
+#include <deal.II/fe/fe_abf.h>
+#include <deal.II/fe/fe_bernardi_raugel.h>
+#include <deal.II/fe/fe_dgq.h>
+#include <deal.II/fe/fe_q.h>
+#include <deal.II/fe/fe_raviart_thomas.h>
+#include <deal.II/fe/fe_system.h>
+#include <deal.II/fe/fe_values.h>
+#include <deal.II/fe/mapping_q.h>
+#include <deal.II/fe/mapping_q1_eulerian.h>
+
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/grid_out.h>
+
+#include <deal.II/lac/constraint_matrix.h>
+#include <deal.II/lac/precondition.h>
+#include <deal.II/lac/solver_cg.h>
+#include <deal.II/lac/sparse_matrix.h>
+#include <deal.II/lac/sparsity_pattern.h>
+#include <deal.II/lac/vector.h>
+#include <deal.II/lac/vector_memory.h>
+
+#include <deal.II/numerics/data_out.h>
+#include <deal.II/numerics/matrix_tools.h>
+#include <deal.II/numerics/vector_tools.h>
+
+
+
+template <int dim>
+class TestMap1 : public Function<dim>
+{
+public:
+  TestMap1(const unsigned int n_components)
+    : Function<dim>(n_components)
+  {}
+
+  virtual ~TestMap1()
+  {}
+
+  virtual double
+  value(const Point<dim> &p, const unsigned int component = 0) const;
+
+  void
+  vector_value(const Point<dim> &p, Vector<double> &return_value) const;
+};
+
+
+
+template <int dim>
+double
+TestMap1<dim>::value(const Point<dim> &p, const unsigned int component) const
+{
+  if (component == 0)
+    return (p(0) * p(0));
+  if (component == 1)
+    return (p(1) * p(1));
+
+  return (0);
+}
+
+
+template <int dim>
+void
+TestMap1<dim>::vector_value(const Point<dim> &p,
+                            Vector<double> &  return_value) const
+{
+  Assert(return_value.size() == this->n_components,
+         ExcDimensionMismatch(return_value.size(), this->n_components));
+
+  for (unsigned int iCount = 0; iCount < this->n_components; iCount++)
+    return_value(iCount) = value(p, iCount);
+}
+
+
+
+///-----------------------------------------------------------------------
+
+template <int dim>
+class TestDef1 : public Function<dim>
+{
+private:
+  const double phi;
+
+public:
+  TestDef1(const unsigned int n_components, const double ph)
+    : Function<dim>(n_components)
+    , phi(ph)
+  {}
+
+  virtual ~TestDef1()
+  {}
+
+  virtual double
+  value(const Point<dim> &p, const unsigned int component = 0) const;
+
+  void
+  vector_value(const Point<dim> &p, Vector<double> &return_value) const;
+};
+
+
+
+template <int dim>
+double
+TestDef1<dim>::value(const Point<dim> &p, const unsigned int component) const
+{
+  Point<2> center;
+  center(0)    = 0.5;
+  center(1)    = 0.5;
+  double rad   = p.distance(center),
+         phi_p = atan2(p(0) - center(0), p(1) - center(1));
+
+  if (component == 0)
+    return rad * (sin(phi + phi_p) - sin(phi_p));
+  else
+    return rad * (cos(phi + phi_p) - cos(phi_p));
+}
+
+
+template <int dim>
+void
+TestDef1<dim>::vector_value(const Point<dim> &p,
+                            Vector<double> &  return_value) const
+{
+  Assert(return_value.size() == this->n_components,
+         ExcDimensionMismatch(return_value.size(), this->n_components));
+  for (unsigned int iCount = 0; iCount < this->n_components; iCount++)
+    return_value(iCount) = value(p, iCount);
+}
+
+
+///-----------------------------------------------------------------------
+
+
+template <int dim>
+class TestDef2 : public Function<dim>
+{
+private:
+  const double scale;
+
+public:
+  TestDef2(const unsigned int n_components, const double sc)
+    : Function<dim>(n_components)
+    , scale(sc)
+  {}
+
+  virtual ~TestDef2()
+  {}
+
+  virtual double
+  value(const Point<dim> &p, const unsigned int component = 0) const;
+
+  void
+  vector_value(const Point<dim> &p, Vector<double> &return_value) const;
+};
+
+
+template <int dim>
+double
+TestDef2<dim>::value(const Point<dim> &p, const unsigned int component) const
+{
+  double x = p(0), y = p(1);
+
+  if (component == 0)
+    return scale * x;
+  else
+    return scale * y;
+}
+
+
+template <int dim>
+void
+TestDef2<dim>::vector_value(const Point<dim> &p,
+                            Vector<double> &  return_value) const
+{
+  Assert(return_value.size() == this->n_components,
+         ExcDimensionMismatch(return_value.size(), this->n_components));
+  for (unsigned int iCount = 0; iCount < this->n_components; iCount++)
+    return_value(iCount) = value(p, iCount);
+}
+
+
+///-----------------------------------------------------------------------
+// testDef3 implements parallelograms ...
+
+
+template <int dim>
+class TestDef3 : public Function<dim>
+{
+private:
+  const double scale;
+
+public:
+  TestDef3(const unsigned int n_components, const double sc)
+    : Function<dim>(n_components)
+    , scale(sc)
+  {}
+
+  virtual ~TestDef3()
+  {}
+
+  virtual double
+  value(const Point<dim> &p, const unsigned int component = 0) const;
+
+  void
+  vector_value(const Point<dim> &p, Vector<double> &return_value) const;
+};
+
+
+template <int dim>
+double
+TestDef3<dim>::value(const Point<dim> &p, const unsigned int component) const
+{
+  double y = p(1);
+
+  if (component == 0)
+    return scale * y;
+  else
+    return 0;
+}
+
+
+template <int dim>
+void
+TestDef3<dim>::vector_value(const Point<dim> &p,
+                            Vector<double> &  return_value) const
+{
+  Assert(return_value.size() == this->n_components,
+         ExcDimensionMismatch(return_value.size(), this->n_components));
+  for (unsigned int iCount = 0; iCount < this->n_components; iCount++)
+    return_value(iCount) = value(p, iCount);
+}
+
+template <int dim>
+class TestPoly : public Function<dim>
+{
+private:
+  std::vector<Polynomials::Polynomial<double>> polys;
+
+public:
+  TestPoly(unsigned int deg)
+    : Function<dim>(2)
+  {
+    std::vector<double> coeff(deg, 0.0);
+    for (unsigned int p = 0; p < 4; ++p)
+      {
+        for (unsigned int i = 0; i < deg; ++i)
+          {
+            double c = ((double)Testing::rand()) / ((double)RAND_MAX + 1);
+            coeff[i] = c;
+          }
+        polys.push_back(Polynomials::Polynomial<double>(coeff));
+      }
+  }
+
+  virtual ~TestPoly()
+  {}
+
+  virtual double
+  value(const Point<dim> &p, const unsigned int component = 0) const;
+
+  void
+  vector_value(const Point<dim> &p, Vector<double> &return_value) const;
+};
+
+
+template <int dim>
+double
+TestPoly<dim>::value(const Point<dim> &p, const unsigned int component) const
+{
+  double x = p(0), y = p(1);
+
+  if (component == 0)
+    return polys[0].value(x) + polys[1].value(y);
+  else
+    return polys[2].value(x) + polys[3].value(y);
+}
+
+
+template <int dim>
+void
+TestPoly<dim>::vector_value(const Point<dim> &p,
+                            Vector<double> &  return_value) const
+{
+  Assert(return_value.size() == this->n_components,
+         ExcDimensionMismatch(return_value.size(), this->n_components));
+  for (unsigned int iCount = 0; iCount < this->n_components; iCount++)
+    return_value(iCount) = value(p, iCount);
+}
+
+
+
+/*
+ * Check the value of the derivative field.
+ */
+
+double TestProjection(Mapping<2> &mapping, DoFHandler<2> *dof_handler)
+{
+  Vector<double> solution;
+  solution.reinit(dof_handler->n_dofs());
+
+  // Create and Project test function to H_div space and evaluate the error
+  // If the error is in the range of machine precision, this polynomial
+  // degree can obviously be represented by projected field.
+
+  for (unsigned int deg = 1; deg < 4; ++deg)
+    {
+      TestPoly<2> pol(deg);
+
+      // Project solution onto BR FE field
+      ConstraintMatrix hn_constraints;
+      hn_constraints.clear();
+      DoFTools::make_hanging_node_constraints(*dof_handler, hn_constraints);
+      hn_constraints.close();
+      VectorTools::project(
+        mapping, *dof_handler, hn_constraints, QGauss<2>(6), pol, solution);
+
+      // Now evaluate error ...
+      // Use a high order quadrature.
+      QGauss<2>   quad(6);
+      FEValues<2> fe_values(mapping,
+                            dof_handler->get_fe(),
+                            quad,
+                            UpdateFlags(update_values |
+                                        update_quadrature_points |
+                                        update_gradients | update_JxW_values |
+                                        update_contravariant_transformation));
+
+      const unsigned int n_q_points   = quad.size();
+      const unsigned int n_components = dof_handler->get_fe().n_components();
+
+      // Cell iterators
+      DoFHandler<2>::active_cell_iterator cell = dof_handler->begin_active(),
+                                          endc = dof_handler->end();
+
+      double err_u = 0, err_v = 0;
+
+      for (; cell != endc; ++cell)
+        {
+          fe_values.reinit(cell);
+
+          // Get values from solution vector (For Trap.Rule)
+          std::vector<Vector<double>> this_value(n_q_points,
+                                                 Vector<double>(n_components));
+          fe_values.get_function_values(solution, this_value);
+
+          for (unsigned int q_point = 0; q_point < n_q_points; ++q_point)
+            {
+              double   u = this_value[q_point](0), v = this_value[q_point](1);
+              Point<2> p = fe_values.quadrature_point(q_point);
+
+              double u_ex = pol.value(p, 0), v_ex = pol.value(p, 1);
+
+              double JxW = fe_values.JxW(q_point);
+
+              err_u += (u - u_ex) * (u - u_ex) * JxW;
+              err_v += (v - v_ex) * (v - v_ex) * JxW;
+            }
+        }
+
+      deallog << dof_handler->get_fe().get_name() << ", testfun(" << deg
+              << "), error_u=" << err_u << ", error_v=" << err_v << std::endl;
+    }
+
+
+  // Test the core functionality
+  DataOut<2> *data_out = new DataOut<2>;
+  data_out->attach_dof_handler(*dof_handler);
+  data_out->add_data_vector(solution, "solution");
+  data_out->build_patches(mapping, 4);
+
+  data_out->write_gnuplot(deallog.get_file_stream());
+
+  delete data_out;
+
+  return (0.0);
+}
+
+
+int
+main()
+{
+  deallog << std::setprecision(PRECISION);
+  deallog << std::fixed;
+  logfile << std::setprecision(PRECISION);
+  logfile << std::fixed;
+  deallog.attach(logfile);
+
+  Triangulation<2> tria_test;
+  DoFHandler<2> *  dof_handler, *dof_handler_def;
+  Point<2>         p1(0, 0), p2(1, 1);
+
+  GridGenerator::hyper_rectangle(tria_test, p1, p2);
+  //  tria_test.refine_global (1);
+  //   GridTools::distort_random (0.4, tria_test);
+
+  // Create a DoFHandler for the BR space
+  FE_BernardiRaugel<2> fe(1);
+  dof_handler = new DoFHandler<2>(tria_test);
+  dof_handler->distribute_dofs(fe);
+
+  QGauss<2> quad_temp(6);
+  deallog << "DoFs per quad: " << fe.dofs_per_quad
+          << ", dofs per line: " << fe.dofs_per_line
+          << ", dofs per vertex: " << fe.dofs_per_vertex << std::endl;
+  deallog << "n_q_points=" << quad_temp.size() << std::endl;
+
+  // Create a deformation object for
+  // the mapping
+  FESystem<2> fe_def(FE_Q<2>(1), 2);
+  dof_handler_def = new DoFHandler<2>(tria_test);
+  dof_handler_def->distribute_dofs(fe_def);
+
+  // Alloc some DoFs
+  Vector<double> solution, solution_q, deformation;
+  solution.reinit(dof_handler->n_dofs());
+  solution_q.reinit(dof_handler->n_dofs());
+  deformation.reinit(dof_handler_def->n_dofs());
+
+  ConstraintMatrix hn_constraints_def;
+  hn_constraints_def.clear();
+  DoFTools::make_hanging_node_constraints(*dof_handler_def, hn_constraints_def);
+  hn_constraints_def.close();
+
+  {
+    MappingQ1Eulerian<2> mapping_euler(*dof_handler_def, deformation);
+
+    // Try rotating the elements
+    for (double rotat = 0; rotat < 2 * numbers::PI; rotat += 0.25 * numbers::PI)
+      {
+        // Rotate element
+        VectorTools::project(*dof_handler_def,
+                             hn_constraints_def,
+                             QGauss<2>(6),
+                             TestDef1<2>(2, rotat),
+                             deformation);
+        deallog << "phi = " << rotat << std::endl;
+        TestProjection(mapping_euler, dof_handler);
+      }
+
+    // Try resizing the elements
+    for (double scale = -0.75; scale < 4.0; scale += 0.25)
+      {
+        VectorTools::project(*dof_handler_def,
+                             hn_constraints_def,
+                             QGauss<2>(6),
+                             TestDef2<2>(2, scale),
+                             deformation);
+        deallog << "scale = " << scale << std::endl;
+        TestProjection(mapping_euler, dof_handler);
+      }
+
+    // Try paralellogramming the elements
+    for (double scale = -1.0; scale < 1.0; scale += 0.25)
+      {
+        VectorTools::project(*dof_handler_def,
+                             hn_constraints_def,
+                             QGauss<2>(6),
+                             TestDef3<2>(2, scale),
+                             deformation);
+        deallog << "scale = " << scale << std::endl;
+        TestProjection(mapping_euler, dof_handler);
+      }
+
+    // Try arbitrary deformation ...
+    for (unsigned int i = 0; i < deformation.size(); ++i)
+      {
+        double c       = ((double)Testing::rand()) / ((double)RAND_MAX + 1);
+        deformation(i) = 0.35 * (c - 0.5);
+      }
+
+    deallog << "Arbitrary\n" << std::endl;
+    TestProjection(mapping_euler, dof_handler);
+  }
+
+  delete (dof_handler);
+  delete (dof_handler_def);
+
+  return (0);
+}

diff --git a/tests/fe/br_approximation_01.output b/tests/fe/br_approximation_01.output
new file mode 100644 (file)
index 0000000..adb1046
--- /dev/null
+++ b/tests/fe/br_approximation_01.output
@@ -0,0 +1,1516 @@
+
+DEAL::DoFs per quad: 0, dofs per line: 1, dofs per vertex: 2
+DEAL::n_q_points=36
+DEAL::phi = 0.00000000
+DEAL::FE_BR<2>(1), testfun(1), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(2), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(3), error_u=0.00503745, error_v=0.00359278
+# This file was generated by the deal.II library.
+
+
+#
+# For a description of the GNUPLOT format see the GNUPLOT manual.
+#
+# <x> <y> <solution_0> <solution_1> 
+0.00000000 0.00000000 1.12227464 0.25045988 
+0.25000000 0.00000000 1.48868227 0.40322086 
+0.50000000 0.00000000 1.85508990 0.55801946 
+0.75000000 0.00000000 2.22149754 0.71485561 
+1.00000000 0.00000000 2.58790517 0.87372929 
+
+0.00000000 0.25000000 1.32603359 0.48581195 
+0.25000000 0.25000000 1.69244123 0.63857293 
+0.50000000 0.25000000 2.05884886 0.79337156 
+0.75000000 0.25000000 2.42525649 0.95020765 
+1.00000000 0.25000000 2.79166412 1.10908139 
+
+0.00000000 0.50000000 1.61945474 0.72116405 
+0.25000000 0.50000000 1.98586237 0.87392503 
+0.50000000 0.50000000 2.35226989 1.02872360 
+0.75000000 0.50000000 2.71867776 1.18555975 
+1.00000000 0.50000000 3.08508539 1.34443343 
+
+0.00000000 0.75000000 2.00253797 0.95651609 
+0.25000000 0.75000000 2.36894560 1.10927713 
+0.50000000 0.75000000 2.73535323 1.26407564 
+0.75000000 0.75000000 3.10176086 1.42091179 
+1.00000000 0.75000000 3.46816850 1.57978559 
+
+0.00000000 1.00000000 2.47528315 1.19186819 
+0.25000000 1.00000000 2.84169102 1.34462917 
+0.50000000 1.00000000 3.20809865 1.49942780 
+0.75000000 1.00000000 3.57450628 1.65626395 
+1.00000000 1.00000000 3.94091392 1.81513762 
+
+
+DEAL::phi = 0.78539816
+DEAL::FE_BR<2>(1), testfun(1), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(2), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(3), error_u=0.00156772, error_v=0.00200781
+# This file was generated by the deal.II library.
+
+
+#
+# For a description of the GNUPLOT format see the GNUPLOT manual.
+#
+# <x> <y> <solution_0> <solution_1> 
+-0.20710678 0.50000000 1.44333446 1.11362123 
+-0.03033009 0.32322329 1.49746406 0.98280144 
+0.14644662 0.14644662 1.55159378 0.92712802 
+0.32322329 -0.03033009 1.60572350 0.94660085 
+0.50000000 -0.20710678 1.65985310 1.04122007 
+
+-0.03033009 0.67677671 1.85629940 1.70601964 
+0.14644662 0.50000000 1.88059175 1.53546786 
+0.32322329 0.32322329 1.90488410 1.44006240 
+0.50000000 0.14644662 1.92917645 1.41980326 
+0.67677671 -0.03033009 1.95346880 1.47469056 
+
+0.14644662 0.85355341 2.33566618 2.29841805 
+0.32322329 0.67677671 2.33012128 2.08813429 
+0.50000000 0.50000000 2.32457638 1.95299685 
+0.67677671 0.32322329 2.31903124 1.89300573 
+0.85355341 0.14644662 2.31348634 1.90816092 
+
+0.32322329 1.03033006 2.88143492 2.89081645 
+0.50000000 0.85355341 2.84605265 2.64080071 
+0.67677671 0.67677671 2.81067038 2.46593118 
+0.85355341 0.50000000 2.77528811 2.36620808 
+1.03033006 0.32322329 2.73990583 2.34163141 
+
+0.50000000 1.20710683 3.49360561 3.48321462 
+0.67677671 1.03033006 3.42838597 3.19346690 
+0.85355341 0.85355341 3.36316633 2.97886562 
+1.03033006 0.67677671 3.29794693 2.83941054 
+1.20710683 0.50000000 3.23272729 2.77510190 
+
+
+DEAL::phi = 1.57079633
+DEAL::FE_BR<2>(1), testfun(1), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(2), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(3), error_u=0.00161856, error_v=0.00145940
+# This file was generated by the deal.II library.
+
+
+#
+# For a description of the GNUPLOT format see the GNUPLOT manual.
+#
+# <x> <y> <solution_0> <solution_1> 
+0.00000000 1.00000000 1.80566573 1.52839494 
+0.00000000 0.75000000 1.60405922 1.37830818 
+0.00000000 0.50000000 1.40245271 1.23313153 
+0.00000000 0.25000000 1.20084620 1.09286475 
+0.00000000 0.00000000 0.99923968 0.95750815 
+
+0.25000000 1.00000000 2.10471225 1.84659100 
+0.25000000 0.75000000 1.90310574 1.69650424 
+0.25000000 0.50000000 1.70149922 1.55132747 
+0.25000000 0.25000000 1.49989271 1.41106081 
+0.25000000 0.00000000 1.29828620 1.27570415 
+
+0.50000000 1.00000000 2.51653481 2.16478705 
+0.50000000 0.75000000 2.31492829 2.01470017 
+0.50000000 0.50000000 2.11332178 1.86952353 
+0.50000000 0.25000000 1.91171527 1.72925687 
+0.50000000 0.00000000 1.71010876 1.59390020 
+
+0.75000000 1.00000000 3.04113340 2.48298311 
+0.75000000 0.75000000 2.83952689 2.33289623 
+0.75000000 0.50000000 2.63792038 2.18771958 
+0.75000000 0.25000000 2.43631387 2.04745293 
+0.75000000 0.00000000 2.23470736 1.91209626 
+
+1.00000000 1.00000000 3.67850804 2.80117917 
+1.00000000 0.75000000 3.47690153 2.65109229 
+1.00000000 0.50000000 3.27529502 2.50591564 
+1.00000000 0.25000000 3.07368851 2.36564898 
+1.00000000 0.00000000 2.87208200 2.23029232 
+
+
+DEAL::phi = 2.35619449
+DEAL::FE_BR<2>(1), testfun(1), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(2), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(3), error_u=0.00116443, error_v=0.00347282
+# This file was generated by the deal.II library.
+
+
+#
+# For a description of the GNUPLOT format see the GNUPLOT manual.
+#
+# <x> <y> <solution_0> <solution_1> 
+0.50000000 1.20710683 3.29215455 4.01893616 
+0.32322329 1.03033006 2.95274687 3.37606454 
+0.14644662 0.85355341 2.61333919 2.83202219 
+-0.03033009 0.67677671 2.27393174 2.38680959 
+-0.20710678 0.50000000 1.93452406 2.04042673 
+
+0.67677671 1.03033006 3.06465006 3.96481657 
+0.50000000 0.85355341 2.75384879 3.33861136 
+0.32322329 0.67677671 2.44304752 2.81123590 
+0.14644662 0.50000000 2.13224626 2.38268995 
+-0.03033009 0.32322329 1.82144511 2.05297351 
+
+0.85355341 0.85355341 2.89437294 3.91069698 
+0.67677671 0.67677671 2.61217809 3.30115843 
+0.50000000 0.50000000 2.32998323 2.79044938 
+0.32322329 0.32322329 2.04778838 2.37857008 
+0.14644662 0.14644662 1.76559353 2.06552029 
+
+1.03033006 0.67677671 2.78132343 3.85657740 
+0.85355341 0.50000000 2.52773499 3.26370549 
+0.67677671 0.32322329 2.27414632 2.76966310 
+0.50000000 0.14644662 2.02055788 2.37445045 
+0.32322329 -0.03033009 1.76696932 2.07806730 
+
+1.20710683 0.50000000 2.72550106 3.80245781 
+1.03033006 0.32322329 2.50051904 3.22625256 
+0.85355341 0.14644662 2.27553678 2.74887681 
+0.67677671 -0.03033009 2.05055451 2.37033057 
+0.50000000 -0.20710678 1.82557249 2.09061408 
+
+
+DEAL::phi = 3.14159265
+DEAL::FE_BR<2>(1), testfun(1), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(2), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(3), error_u=0.00343222, error_v=0.00456830
+# This file was generated by the deal.II library.
+
+
+#
+# For a description of the GNUPLOT format see the GNUPLOT manual.
+#
+# <x> <y> <solution_0> <solution_1> 
+1.00000000 1.00000000 2.53625584 2.36198974 
+0.75000000 1.00000000 2.26949024 2.04948711 
+0.50000000 1.00000000 2.00272489 1.80653965 
+0.25000000 1.00000000 1.73595953 1.63314784 
+0.00000000 1.00000000 1.46919417 1.52931142 
+
+1.00000000 0.75000000 2.32557559 2.09288716 
+0.75000000 0.75000000 2.05881023 1.78038430 
+0.50000000 0.75000000 1.79204488 1.53743696 
+0.25000000 0.75000000 1.52527952 1.36404502 
+0.00000000 0.75000000 1.25851417 1.26020861 
+
+1.00000000 0.50000000 2.14315891 1.82378435 
+0.75000000 0.50000000 1.87639356 1.51128149 
+0.50000000 0.50000000 1.60962820 1.26833415 
+0.25000000 0.50000000 1.34286284 1.09494233 
+0.00000000 0.50000000 1.07609749 0.99110591 
+
+1.00000000 0.25000000 1.98900557 1.55468154 
+0.75000000 0.25000000 1.72224021 1.24217880 
+0.50000000 0.25000000 1.45547485 0.99923146 
+0.25000000 0.25000000 1.18870950 0.82583958 
+0.00000000 0.25000000 0.92194408 0.72200316 
+
+1.00000000 0.00000000 1.86311555 1.28557885 
+0.75000000 0.00000000 1.59635019 0.97307605 
+0.50000000 0.00000000 1.32958472 0.73012865 
+0.25000000 0.00000000 1.06281936 0.55673683 
+0.00000000 0.00000000 0.79605401 0.45290041 
+
+
+DEAL::phi = 3.92699082
+DEAL::FE_BR<2>(1), testfun(1), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(2), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(3), error_u=0.00124257, error_v=0.00049351
+# This file was generated by the deal.II library.
+
+
+#
+# For a description of the GNUPLOT format see the GNUPLOT manual.
+#
+# <x> <y> <solution_0> <solution_1> 
+1.20710683 0.50000000 2.01600075 2.22916555 
+1.03033006 0.67677671 2.18843865 2.18576097 
+0.85355341 0.85355341 2.36087632 2.17961192 
+0.67677671 1.03033006 2.53331399 2.21071887 
+0.50000000 1.20710683 2.70575190 2.27908158 
+
+1.03033006 0.32322329 1.77486801 2.03867221 
+0.85355341 0.50000000 1.90723825 1.96732795 
+0.67677671 0.67677671 2.03960848 1.93323934 
+0.50000000 0.85355341 2.17197871 1.93640673 
+0.32322329 1.03033006 2.30434871 1.97682989 
+
+0.85355341 0.14644662 1.59285140 1.84817886 
+0.67677671 0.32322329 1.68515408 1.74889493 
+0.50000000 0.50000000 1.77745676 1.68686676 
+0.32322329 0.67677671 1.86975944 1.66209447 
+0.14644662 0.85355341 1.96206212 1.67457807 
+
+0.67677671 -0.03033009 1.46995103 1.65768540 
+0.50000000 0.14644662 1.52218616 1.53046191 
+0.32322329 0.32322329 1.57442129 1.44049418 
+0.14644662 0.50000000 1.62665641 1.38778234 
+-0.03033009 0.67677671 1.67889154 1.37232625 
+
+0.50000000 -0.20710678 1.40616691 1.46719205 
+0.32322329 -0.03033009 1.41833448 1.31202888 
+0.14644662 0.14644662 1.43050218 1.19412160 
+-0.03033009 0.32322329 1.44266975 1.11347020 
+-0.20710678 0.50000000 1.45483732 1.07007444 
+
+
+DEAL::phi = 4.71238898
+DEAL::FE_BR<2>(1), testfun(1), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(2), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(3), error_u=0.00317168, error_v=0.00555548
+# This file was generated by the deal.II library.
+
+
+#
+# For a description of the GNUPLOT format see the GNUPLOT manual.
+#
+# <x> <y> <solution_0> <solution_1> 
+1.00000000 0.00000000 1.42972910 1.24740255 
+1.00000000 0.25000000 1.76195395 1.47773325 
+1.00000000 0.50000000 2.09417892 1.72374749 
+1.00000000 0.75000000 2.42640376 1.98544526 
+1.00000000 1.00000000 2.75862861 2.26282668 
+
+0.75000000 0.00000000 1.17669392 0.95795238 
+0.75000000 0.25000000 1.50891876 1.18828309 
+0.75000000 0.50000000 1.84114361 1.43429732 
+0.75000000 0.75000000 2.17336845 1.69599509 
+0.75000000 1.00000000 2.50559330 1.97337651 
+
+0.50000000 0.00000000 0.98133618 0.66850221 
+0.50000000 0.25000000 1.31356108 0.89883286 
+0.50000000 0.50000000 1.64578593 1.14484715 
+0.50000000 0.75000000 1.97801077 1.40654492 
+0.50000000 1.00000000 2.31023574 1.68392634 
+
+0.25000000 0.00000000 0.84365606 0.37905201 
+0.25000000 0.25000000 1.17588091 0.60938269 
+0.25000000 0.50000000 1.50810587 0.85539693 
+0.25000000 0.75000000 1.84033072 1.11709476 
+0.25000000 1.00000000 2.17255545 1.39447618 
+
+0.00000000 0.00000000 0.76365352 0.08960184 
+0.00000000 0.25000000 1.09587836 0.31993252 
+0.00000000 0.50000000 1.42810333 0.56594676 
+0.00000000 0.75000000 1.76032817 0.82764459 
+0.00000000 1.00000000 2.09255290 1.10502601 
+
+
+DEAL::phi = 5.49778714
+DEAL::FE_BR<2>(1), testfun(1), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(2), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(3), error_u=0.00064047, error_v=0.00194015
+# This file was generated by the deal.II library.
+
+
+#
+# For a description of the GNUPLOT format see the GNUPLOT manual.
+#
+# <x> <y> <solution_0> <solution_1> 
+0.50000000 -0.20710678 1.03809333 1.79741383 
+0.67677671 -0.03033009 1.43729138 2.05974579 
+0.85355341 0.14644662 1.83648944 2.39594722 
+1.03033006 0.32322329 2.23568749 2.80601811 
+1.20710683 0.50000000 2.63488555 3.28995800 
+
+0.32322329 -0.03033009 0.97343618 1.79522145 
+0.50000000 0.14644662 1.34264731 2.09338593 
+0.67677671 0.32322329 1.71185851 2.46541977 
+0.85355341 0.50000000 2.08106971 2.91132307 
+1.03033006 0.67677671 2.45028090 3.43109536 
+
+0.14644662 0.14644662 0.95122093 1.79302919 
+0.32322329 0.32322329 1.29044521 2.12702608 
+0.50000000 0.50000000 1.62966955 2.53489232 
+0.67677671 0.67677671 1.96889389 3.01662803 
+0.85355341 0.85355341 2.30811810 3.57223272 
+
+-0.03033009 0.32322329 0.97144753 1.79083681 
+0.14644662 0.50000000 1.28068495 2.16066623 
+0.32322329 0.67677671 1.58992243 2.60436487 
+0.50000000 0.85355341 1.89915991 3.12193274 
+0.67677671 1.03033006 2.20839739 3.71337008 
+
+-0.20710678 0.50000000 1.03411603 1.78864455 
+-0.03033009 0.67677671 1.31336653 2.19430637 
+0.14644662 0.85355341 1.59261715 2.67383742 
+0.32322329 1.03033006 1.87186778 3.22723770 
+0.50000000 1.20710683 2.15111828 3.85450745 
+
+
+DEAL::scale = -0.75000000
+DEAL::FE_BR<2>(1), testfun(1), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(2), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(3), error_u=0.00000004, error_v=0.00000014
+# This file was generated by the deal.II library.
+
+
+#
+# For a description of the GNUPLOT format see the GNUPLOT manual.
+#
+# <x> <y> <solution_0> <solution_1> 
+0.00000000 0.00000000 1.49518418 0.87554324 
+0.06250000 0.00000000 1.52882481 0.89350492 
+0.12500000 0.00000000 1.56246543 0.91638440 
+0.18750000 0.00000000 1.59610617 0.94418168 
+0.25000000 0.00000000 1.62974679 0.97689676 
+
+0.00000000 0.06250000 1.55104423 0.92428309 
+0.06250000 0.06250000 1.58468485 0.94224471 
+0.12500000 0.06250000 1.61832559 0.96512419 
+0.18750000 0.06250000 1.65196621 0.99292147 
+0.25000000 0.06250000 1.68560684 1.02563655 
+
+0.00000000 0.12500000 1.60750580 0.97302288 
+0.06250000 0.12500000 1.64114642 0.99098450 
+0.12500000 0.12500000 1.67478716 1.01386404 
+0.18750000 0.12500000 1.70842779 1.04166126 
+0.25000000 0.12500000 1.74206841 1.07437634 
+
+0.00000000 0.18750000 1.66456890 1.02176261 
+0.06250000 0.18750000 1.69820952 1.03972435 
+0.12500000 0.18750000 1.73185027 1.06260383 
+0.18750000 0.18750000 1.76549089 1.09040105 
+0.25000000 0.18750000 1.79913151 1.12311614 
+
+0.00000000 0.25000000 1.72223353 1.07050240 
+0.06250000 0.25000000 1.75587416 1.08846414 
+0.12500000 0.25000000 1.78951478 1.11134362 
+0.18750000 0.25000000 1.82315552 1.13914084 
+0.25000000 0.25000000 1.85679615 1.17185593 
+
+
+DEAL::scale = -0.50000000
+DEAL::FE_BR<2>(1), testfun(1), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(2), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(3), error_u=0.00007741, error_v=0.00000475
+# This file was generated by the deal.II library.
+
+
+#
+# For a description of the GNUPLOT format see the GNUPLOT manual.
+#
+# <x> <y> <solution_0> <solution_1> 
+0.00000000 0.00000000 0.88305438 1.02324915 
+0.12500000 0.00000000 1.01614177 1.02904272 
+0.25000000 0.00000000 1.14922917 1.04561591 
+0.37500000 0.00000000 1.28231657 1.07296848 
+0.50000000 0.00000000 1.41540384 1.11110055 
+
+0.00000000 0.12500000 0.93834335 1.14202273 
+0.12500000 0.12500000 1.07143068 1.14781642 
+0.25000000 0.12500000 1.20451808 1.16438949 
+0.37500000 0.12500000 1.33760548 1.19174218 
+0.50000000 0.12500000 1.47069287 1.22987425 
+
+0.00000000 0.25000000 1.02012241 1.26079643 
+0.12500000 0.25000000 1.15320981 1.26659012 
+0.25000000 0.25000000 1.28629720 1.28316319 
+0.37500000 0.25000000 1.41938460 1.31051576 
+0.50000000 0.25000000 1.55247200 1.34864783 
+
+0.00000000 0.37500000 1.12839174 1.37957001 
+0.12500000 0.37500000 1.26147902 1.38536370 
+0.25000000 0.37500000 1.39456642 1.40193689 
+0.37500000 0.37500000 1.52765381 1.42928946 
+0.50000000 0.37500000 1.66074121 1.46742153 
+
+0.00000000 0.50000000 1.26315105 1.49834371 
+0.12500000 0.50000000 1.39623845 1.50413740 
+0.25000000 0.50000000 1.52932584 1.52071047 
+0.37500000 0.50000000 1.66241324 1.54806304 
+0.50000000 0.50000000 1.79550052 1.58619511 
+
+
+DEAL::scale = -0.25000000
+DEAL::FE_BR<2>(1), testfun(1), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(2), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(3), error_u=0.00036684, error_v=0.00006544
+# This file was generated by the deal.II library.
+
+
+#
+# For a description of the GNUPLOT format see the GNUPLOT manual.
+#
+# <x> <y> <solution_0> <solution_1> 
+0.00000000 0.00000000 0.91717011 1.40107632 
+0.18750000 0.00000000 1.03744233 1.47136712 
+0.37500000 0.00000000 1.15771449 1.60640967 
+0.56250000 0.00000000 1.27798676 1.80620408 
+0.75000000 0.00000000 1.39825892 2.07075024 
+
+0.00000000 0.18750000 1.06572628 1.55971622 
+0.18750000 0.18750000 1.18599844 1.63000703 
+0.37500000 0.18750000 1.30627072 1.76504958 
+0.56250000 0.18750000 1.42654288 1.96484399 
+0.75000000 0.18750000 1.54681516 2.22939014 
+
+0.00000000 0.37500000 1.23737121 1.71835613 
+0.18750000 0.37500000 1.35764349 1.78864694 
+0.37500000 0.37500000 1.47791564 1.92368948 
+0.56250000 0.37500000 1.59818792 2.12348390 
+0.75000000 0.37500000 1.71846008 2.38803005 
+
+0.00000000 0.56250000 1.43210506 1.87699604 
+0.18750000 0.56250000 1.55237734 1.94728684 
+0.37500000 0.56250000 1.67264950 2.08232951 
+0.56250000 0.56250000 1.79292178 2.28212380 
+0.75000000 0.56250000 1.91319394 2.54666996 
+
+0.00000000 0.75000000 1.64992774 2.03563595 
+0.18750000 0.75000000 1.77019989 2.10592675 
+0.37500000 0.75000000 1.89047217 2.24096918 
+0.56250000 0.75000000 2.01074433 2.44076371 
+0.75000000 0.75000000 2.13101673 2.70530987 
+
+
+DEAL::scale = 0.00000000
+DEAL::FE_BR<2>(1), testfun(1), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(2), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(3), error_u=0.00060369, error_v=0.00469129
+# This file was generated by the deal.II library.
+
+
+#
+# For a description of the GNUPLOT format see the GNUPLOT manual.
+#
+# <x> <y> <solution_0> <solution_1> 
+0.00000000 0.00000000 0.91057789 1.11073303 
+0.25000000 0.00000000 1.06508327 1.20536542 
+0.50000000 0.00000000 1.21958864 1.32352281 
+0.75000000 0.00000000 1.37409401 1.46520543 
+1.00000000 0.00000000 1.52859938 1.63041317 
+
+0.00000000 0.25000000 1.15689230 1.58012486 
+0.25000000 0.25000000 1.31139767 1.67475724 
+0.50000000 0.25000000 1.46590304 1.79291475 
+0.75000000 0.25000000 1.62040842 1.93459725 
+1.00000000 0.25000000 1.77491379 2.09980512 
+
+0.00000000 0.50000000 1.40365410 2.04951668 
+0.25000000 0.50000000 1.55815947 2.14414907 
+0.50000000 0.50000000 1.71266484 2.26230645 
+0.75000000 0.50000000 1.86717021 2.40398908 
+1.00000000 0.50000000 2.02167559 2.56919694 
+
+0.00000000 0.75000000 1.65086317 2.51890850 
+0.25000000 0.75000000 1.80536854 2.61354089 
+0.50000000 0.75000000 1.95987391 2.73169827 
+0.75000000 0.75000000 2.11437941 2.87338090 
+1.00000000 0.75000000 2.26888466 3.03858876 
+
+0.00000000 1.00000000 1.89851964 2.98830032 
+0.25000000 1.00000000 2.05302501 3.08293271 
+0.50000000 1.00000000 2.20753050 3.20109010 
+0.75000000 1.00000000 2.36203575 3.34277272 
+1.00000000 1.00000000 2.51654124 3.50798059 
+
+
+DEAL::scale = 0.25000000
+DEAL::FE_BR<2>(1), testfun(1), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(2), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(3), error_u=0.01753596, error_v=0.01527368
+# This file was generated by the deal.II library.
+
+
+#
+# For a description of the GNUPLOT format see the GNUPLOT manual.
+#
+# <x> <y> <solution_0> <solution_1> 
+0.00000000 0.00000000 0.93438125 0.43407688 
+0.31250000 0.00000000 1.57250190 0.60410565 
+0.62500000 0.00000000 2.21062255 0.94299752 
+0.93750000 0.00000000 2.84874320 1.45075250 
+1.25000000 0.00000000 3.48686385 2.12737036 
+
+0.00000000 0.31250000 1.14632070 0.91058934 
+0.31250000 0.31250000 1.78444135 1.08061814 
+0.62500000 0.31250000 2.42256212 1.41951001 
+0.93750000 0.31250000 3.06068277 1.92726493 
+1.25000000 0.31250000 3.69880342 2.60388303 
+
+0.00000000 0.62500000 1.47079909 1.38710177 
+0.31250000 0.62500000 2.10891986 1.55713058 
+0.62500000 0.62500000 2.74704051 1.89602244 
+0.93750000 0.62500000 3.38516116 2.40377736 
+1.25000000 0.62500000 4.02328205 3.08039546 
+
+0.00000000 0.93750000 1.90781653 1.86361420 
+0.31250000 0.93750000 2.54593730 2.03364301 
+0.62500000 0.93750000 3.18405795 2.37253499 
+0.93750000 0.93750000 3.82217860 2.88028979 
+1.25000000 0.93750000 4.46029949 3.55690789 
+
+0.00000000 1.25000000 2.45737290 2.34012675 
+0.31250000 1.25000000 3.09549356 2.51015544 
+0.62500000 1.25000000 3.73361421 2.84904742 
+0.93750000 1.25000000 4.37173510 3.35680223 
+1.25000000 1.25000000 5.00985575 4.03342009 
+
+
+DEAL::scale = 0.50000000
+DEAL::FE_BR<2>(1), testfun(1), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(2), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(3), error_u=0.00120930, error_v=0.00710054
+# This file was generated by the deal.II library.
+
+
+#
+# For a description of the GNUPLOT format see the GNUPLOT manual.
+#
+# <x> <y> <solution_0> <solution_1> 
+0.00000000 0.00000000 0.80712867 1.60099792 
+0.37500000 0.00000000 0.93035984 1.95196259 
+0.75000000 0.00000000 1.05359101 2.53828502 
+1.12500000 0.00000000 1.17682219 3.35996532 
+1.50000000 0.00000000 1.30005336 4.41700363 
+
+0.00000000 0.37500000 1.05997908 1.97544742 
+0.37500000 0.37500000 1.18321025 2.32641196 
+0.75000000 0.37500000 1.30644143 2.91273451 
+1.12500000 0.37500000 1.42967260 3.73441482 
+1.50000000 0.37500000 1.55290377 4.79145288 
+
+0.00000000 0.75000000 1.57492507 2.34989691 
+0.37500000 0.75000000 1.69815624 2.70086145 
+0.75000000 0.75000000 1.82138741 3.28718400 
+1.12500000 0.75000000 1.94461858 4.10886431 
+1.50000000 0.75000000 2.06784964 5.16590261 
+
+0.00000000 1.12500000 2.35196662 2.72434640 
+0.37500000 1.12500000 2.47519779 3.07531095 
+0.75000000 1.12500000 2.59842896 3.66163349 
+1.12500000 1.12500000 2.72166014 4.48331404 
+1.50000000 1.12500000 2.84489131 5.54035187 
+
+0.00000000 1.50000000 3.39110351 3.09879589 
+0.37500000 1.50000000 3.51433468 3.44976044 
+0.75000000 1.50000000 3.63756585 4.03608322 
+1.12500000 1.50000000 3.76079702 4.85776329 
+1.50000000 1.50000000 3.88402820 5.91480160 
+
+
+DEAL::scale = 0.75000000
+DEAL::FE_BR<2>(1), testfun(1), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(2), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(3), error_u=0.05434282, error_v=0.00689333
+# This file was generated by the deal.II library.
+
+
+#
+# For a description of the GNUPLOT format see the GNUPLOT manual.
+#
+# <x> <y> <solution_0> <solution_1> 
+0.00000000 0.00000000 0.39492503 1.00700533 
+0.43750000 0.00000000 1.25056243 1.24483061 
+0.87500000 0.00000000 2.10619998 1.82069337 
+1.31250000 0.00000000 2.96183729 2.73459339 
+1.75000000 0.00000000 3.81747460 3.98653102 
+
+0.00000000 0.43750000 0.82893574 1.39263582 
+0.43750000 0.43750000 1.68457317 1.63046110 
+0.87500000 0.43750000 2.54021049 2.20632386 
+1.31250000 0.43750000 3.39584804 3.12022400 
+1.75000000 0.43750000 4.25148535 4.37216139 
+
+0.00000000 0.87500000 1.55456448 1.77826619 
+0.43750000 0.87500000 2.41020179 2.01609159 
+0.87500000 0.87500000 3.26583934 2.59195423 
+1.31250000 0.87500000 4.12147665 3.50585437 
+1.75000000 0.87500000 4.97711420 4.75779200 
+
+0.00000000 1.31250000 2.57181120 2.16389656 
+0.43750000 1.31250000 3.42744875 2.40172195 
+0.87500000 1.31250000 4.28308630 2.97758460 
+1.31250000 1.31250000 5.13872337 3.89148474 
+1.75000000 1.31250000 5.99436092 5.14342260 
+
+0.00000000 1.75000000 3.88067627 2.54952717 
+0.43750000 1.75000000 4.73631382 2.78735232 
+0.87500000 1.75000000 5.59195089 3.36321521 
+1.31250000 1.75000000 6.44758844 4.27711535 
+1.75000000 1.75000000 7.30322599 5.52905273 
+
+
+DEAL::scale = 1.00000000
+DEAL::FE_BR<2>(1), testfun(1), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(2), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(3), error_u=0.21814424, error_v=0.17818144
+# This file was generated by the deal.II library.
+
+
+#
+# For a description of the GNUPLOT format see the GNUPLOT manual.
+#
+# <x> <y> <solution_0> <solution_1> 
+0.00000000 0.00000000 0.66298616 0.84270054 
+0.50000000 0.00000000 1.44897246 1.21549404 
+1.00000000 0.00000000 2.23495865 1.61286879 
+1.50000000 0.00000000 3.02094507 2.03482485 
+2.00000000 0.00000000 3.80693126 2.48136187 
+
+0.00000000 0.50000000 0.83849216 2.04384327 
+0.50000000 0.50000000 1.62447846 2.41663671 
+1.00000000 0.50000000 2.41046476 2.81401134 
+1.50000000 0.50000000 3.19645095 3.23596740 
+2.00000000 0.50000000 3.98243713 3.68250465 
+
+0.00000000 1.00000000 1.07133210 3.24498582 
+0.50000000 1.00000000 1.85731828 3.61777925 
+1.00000000 1.00000000 2.64330459 4.01515388 
+1.50000000 1.00000000 3.42929077 4.43710995 
+2.00000000 1.00000000 4.21527719 4.88364744 
+
+0.00000000 1.50000000 1.36150587 4.44612837 
+0.50000000 1.50000000 2.14749217 4.81892204 
+1.00000000 1.50000000 2.93347836 5.21629667 
+1.50000000 1.50000000 3.71946478 5.63825274 
+2.00000000 1.50000000 4.50545073 6.08478975 
+
+0.00000000 2.00000000 1.70901358 5.64727116 
+0.50000000 2.00000000 2.49499989 6.02006483 
+1.00000000 2.00000000 3.28098607 6.41743946 
+1.50000000 2.00000000 4.06697226 6.83939552 
+2.00000000 2.00000000 4.85295868 7.28593254 
+
+
+DEAL::scale = 1.25000000
+DEAL::FE_BR<2>(1), testfun(1), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(2), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(3), error_u=0.34524765, error_v=0.56931911
+# This file was generated by the deal.II library.
+
+
+#
+# For a description of the GNUPLOT format see the GNUPLOT manual.
+#
+# <x> <y> <solution_0> <solution_1> 
+0.00000000 0.00000000 0.31633633 0.19069138 
+0.56250000 0.00000000 1.63148403 0.67703575 
+1.12500000 0.00000000 2.94663167 1.53993213 
+1.68750000 0.00000000 4.26177931 2.77938056 
+2.25000000 0.00000000 5.57692719 4.39538145 
+
+0.00000000 0.56250000 0.56990117 1.48664236 
+0.56250000 0.56250000 1.88504887 1.97298670 
+1.12500000 0.56250000 3.20019650 2.83588314 
+1.68750000 0.56250000 4.51534414 4.07533169 
+2.25000000 0.56250000 5.83049202 5.69133234 
+
+0.00000000 1.12500000 1.19659555 2.78259349 
+0.56250000 1.12500000 2.51174331 3.26893783 
+1.12500000 1.12500000 3.82689095 4.13183403 
+1.68750000 1.12500000 5.14203835 5.37128258 
+2.25000000 1.12500000 6.45718622 6.98728323 
+
+0.00000000 1.68750000 2.19641924 4.07854462 
+0.56250000 1.68750000 3.51156688 4.56488895 
+1.12500000 1.68750000 4.82671452 5.42778540 
+1.68750000 1.68750000 6.14186239 6.66723394 
+2.25000000 1.68750000 7.45701027 8.28323460 
+
+0.00000000 2.25000000 3.56937265 5.37449551 
+0.56250000 2.25000000 4.88452005 5.86083984 
+1.12500000 2.25000000 6.19966793 6.72373629 
+1.68750000 2.25000000 7.51481581 7.96318483 
+2.25000000 2.25000000 8.82996368 9.57918549 
+
+
+DEAL::scale = 1.50000000
+DEAL::FE_BR<2>(1), testfun(1), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(2), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(3), error_u=0.92712085, error_v=0.82151214
+# This file was generated by the deal.II library.
+
+
+#
+# For a description of the GNUPLOT format see the GNUPLOT manual.
+#
+# <x> <y> <solution_0> <solution_1> 
+0.00000000 0.00000000 -0.08865612 -0.43010637 
+0.62500000 0.00000000 1.34410286 0.33669049 
+1.25000000 0.00000000 2.77686191 1.61844516 
+1.87500000 0.00000000 4.20962095 3.41515779 
+2.50000000 0.00000000 5.64237976 5.72682810 
+
+0.00000000 0.62500000 0.47766677 0.94683880 
+0.62500000 0.62500000 1.91042578 1.71363556 
+1.25000000 0.62500000 3.34318471 2.99539042 
+1.87500000 0.62500000 4.77594376 4.79210281 
+2.50000000 0.62500000 6.20870304 7.10377312 
+
+0.00000000 1.25000000 1.73014414 2.32378387 
+0.62500000 1.25000000 3.16290307 3.09058070 
+1.25000000 1.25000000 4.59566212 4.37233543 
+1.87500000 1.25000000 6.02842140 6.16904783 
+2.50000000 1.25000000 7.46118021 8.48071861 
+
+0.00000000 1.87500000 3.66877580 3.70072913 
+0.62500000 1.87500000 5.10153484 4.46752596 
+1.25000000 1.87500000 6.53429413 5.74928045 
+1.87500000 1.87500000 7.96705294 7.54599333 
+2.50000000 1.87500000 9.39981174 9.85766315 
+
+0.00000000 2.50000000 6.29356194 5.07767439 
+0.62500000 2.50000000 7.72632122 5.84447098 
+1.25000000 2.50000000 9.15908051 7.12622595 
+1.87500000 2.50000000 10.59183884 8.92293835 
+2.50000000 2.50000000 12.02459812 11.23460865 
+
+
+DEAL::scale = 1.75000000
+DEAL::FE_BR<2>(1), testfun(1), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(2), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(3), error_u=0.12821310, error_v=1.30658910
+# This file was generated by the deal.II library.
+
+
+#
+# For a description of the GNUPLOT format see the GNUPLOT manual.
+#
+# <x> <y> <solution_0> <solution_1> 
+0.00000000 0.00000000 0.41025513 0.00812389 
+0.68750000 0.00000000 1.14536273 0.19785804 
+1.37500000 0.00000000 1.88047040 0.74701387 
+2.06250000 0.00000000 2.61557794 1.65559137 
+2.75000000 0.00000000 3.35068560 2.92359066 
+
+0.00000000 0.68750000 0.84971792 1.61225343 
+0.68750000 0.68750000 1.58482552 1.80198753 
+1.37500000 0.68750000 2.31993318 2.35114336 
+2.06250000 0.68750000 3.05504084 3.25972080 
+2.75000000 0.68750000 3.79014826 4.52771997 
+
+0.00000000 1.37500000 1.43544292 3.21638298 
+0.68750000 1.37500000 2.17055058 3.40611696 
+1.37500000 1.37500000 2.90565825 3.95527291 
+2.06250000 1.37500000 3.64076591 4.86385012 
+2.75000000 1.37500000 4.37587357 6.13184977 
+
+0.00000000 2.06250000 2.16743040 4.82051229 
+0.68750000 2.06250000 2.90253806 5.01024628 
+1.37500000 2.06250000 3.63764548 5.55940247 
+2.06250000 2.06250000 4.37275314 6.46797991 
+2.75000000 2.06250000 5.10786057 7.73597908 
+
+0.00000000 2.75000000 3.04568005 6.42464209 
+0.68750000 2.75000000 3.78078771 6.61437607 
+1.37500000 2.75000000 4.51589537 7.16353178 
+2.06250000 2.75000000 5.25100279 8.07210922 
+2.75000000 2.75000000 5.98611069 9.34010887 
+
+
+DEAL::scale = 2.00000000
+DEAL::FE_BR<2>(1), testfun(1), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(2), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(3), error_u=1.08887359, error_v=1.90436822
+# This file was generated by the deal.II library.
+
+
+#
+# For a description of the GNUPLOT format see the GNUPLOT manual.
+#
+# <x> <y> <solution_0> <solution_1> 
+0.00000000 0.00000000 0.24138351 -0.19379334 
+0.75000000 0.00000000 1.89006138 0.40055856 
+1.50000000 0.00000000 3.53873920 1.16689575 
+2.25000000 0.00000000 5.18741703 2.10521817 
+3.00000000 0.00000000 6.83609486 3.21552587 
+
+0.00000000 0.75000000 0.91736209 1.39675117 
+0.75000000 0.75000000 2.56604004 1.99110305 
+1.50000000 0.75000000 4.21471786 2.75744033 
+2.25000000 0.75000000 5.86339569 3.69576263 
+3.00000000 0.75000000 7.51207352 4.80607033 
+
+0.00000000 1.50000000 2.40206623 2.98729563 
+0.75000000 1.50000000 4.05074406 3.58164763 
+1.50000000 1.50000000 5.69942188 4.34798479 
+2.25000000 1.50000000 7.34809971 5.28630733 
+3.00000000 1.50000000 8.99677753 6.39661503 
+
+0.00000000 2.25000000 4.69549608 4.57784033 
+0.75000000 2.25000000 6.34417391 5.17219210 
+1.50000000 2.25000000 7.99285173 5.93852901 
+2.25000000 2.25000000 9.64153004 6.87685156 
+3.00000000 2.25000000 11.29020786 7.98715925 
+
+0.00000000 3.00000000 7.79765177 6.16838455 
+0.75000000 3.00000000 9.44632912 6.76273632 
+1.50000000 3.00000000 11.09500694 7.52907372 
+2.25000000 3.00000000 12.74368477 8.46739578 
+3.00000000 3.00000000 14.39236259 9.57770348 
+
+
+DEAL::scale = 2.25000000
+DEAL::FE_BR<2>(1), testfun(1), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(2), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(3), error_u=2.79421326, error_v=0.23911231
+# This file was generated by the deal.II library.
+
+
+#
+# For a description of the GNUPLOT format see the GNUPLOT manual.
+#
+# <x> <y> <solution_0> <solution_1> 
+0.00000000 0.00000000 -0.16951884 0.49635714 
+0.81250000 0.00000000 2.26980972 1.45266056 
+1.62500000 0.00000000 4.70913839 3.50344658 
+2.43750000 0.00000000 7.14846659 6.64871550 
+3.25000000 0.00000000 9.58779526 10.88846684 
+
+0.00000000 0.81250000 0.67251903 1.73564947 
+0.81250000 0.81250000 3.11184764 2.69195294 
+1.62500000 0.81250000 5.55117607 4.74273872 
+2.43750000 0.81250000 7.99050474 7.88800764 
+3.25000000 0.81250000 10.42983341 12.12775898 
+
+0.00000000 1.62500000 1.76048470 2.97494173 
+0.81250000 1.62500000 4.19981337 3.93124509 
+1.62500000 1.62500000 6.63914156 5.98203135 
+2.43750000 1.62500000 9.07847023 9.12730026 
+3.25000000 1.62500000 11.51779842 13.36705112 
+
+0.00000000 2.43750000 3.09437799 4.21423388 
+0.81250000 2.43750000 5.53370667 5.17053747 
+1.62500000 2.43750000 7.97303486 7.22132349 
+2.43750000 2.43750000 10.41236401 10.36659241 
+3.25000000 2.43750000 12.85169220 14.60634422 
+
+0.00000000 3.25000000 4.67419910 5.45352650 
+0.81250000 3.25000000 7.11352777 6.40982962 
+1.62500000 3.25000000 9.55285645 8.46061611 
+2.43750000 3.25000000 11.99218464 11.60588455 
+3.25000000 3.25000000 14.43151283 15.84563637 
+
+
+DEAL::scale = 2.50000000
+DEAL::FE_BR<2>(1), testfun(1), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(2), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(3), error_u=6.76912593, error_v=5.88829482
+# This file was generated by the deal.II library.
+
+
+#
+# For a description of the GNUPLOT format see the GNUPLOT manual.
+#
+# <x> <y> <solution_0> <solution_1> 
+0.00000000 0.00000000 -0.12857348 -0.02527724 
+0.87500000 0.00000000 3.06441641 0.92808962 
+1.75000000 0.00000000 6.25740623 3.22024274 
+2.62500000 0.00000000 9.45039654 6.85118198 
+3.50000000 0.00000000 12.64338589 11.82090759 
+
+0.00000000 0.87500000 1.20850384 2.85820079 
+0.87500000 0.87500000 4.40149355 3.81156778 
+1.75000000 0.87500000 7.59448338 6.10372066 
+2.62500000 0.87500000 10.78747368 9.73466015 
+3.50000000 0.87500000 13.98046303 14.70438576 
+
+0.00000000 1.75000000 4.06963396 5.74167871 
+0.87500000 1.75000000 7.26262426 6.69504595 
+1.75000000 1.75000000 10.45561409 8.98719883 
+2.62500000 1.75000000 13.64860344 12.61813831 
+3.50000000 1.75000000 16.84159279 17.58786392 
+
+0.00000000 2.62500000 8.45481777 8.62515736 
+0.87500000 2.62500000 11.64780712 9.57852364 
+1.75000000 2.62500000 14.84079742 11.87067699 
+2.62500000 2.62500000 18.03378677 15.50161648 
+3.50000000 2.62500000 21.22677612 20.47134209 
+
+0.00000000 3.50000000 14.36405373 11.50863552 
+0.87500000 3.50000000 17.55704308 12.46200180 
+1.75000000 3.50000000 20.75003433 14.75415516 
+2.62500000 3.50000000 23.94302368 18.38509369 
+3.50000000 3.50000000 27.13601303 23.35482025 
+
+
+DEAL::scale = 2.75000000
+DEAL::FE_BR<2>(1), testfun(1), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(2), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(3), error_u=4.48102814, error_v=3.70655457
+# This file was generated by the deal.II library.
+
+
+#
+# For a description of the GNUPLOT format see the GNUPLOT manual.
+#
+# <x> <y> <solution_0> <solution_1> 
+0.00000000 0.00000000 -0.51700091 0.06796724 
+0.93750000 0.00000000 1.98161328 1.28551888 
+1.87500000 0.00000000 4.48022747 3.96664119 
+2.81250000 0.00000000 6.97884130 8.11133385 
+3.75000000 0.00000000 9.47745609 13.71959782 
+
+0.00000000 0.93750000 0.05480351 1.89556301 
+0.93750000 0.93750000 2.55341768 3.11311460 
+1.87500000 0.93750000 5.05203199 5.79423666 
+2.81250000 0.93750000 7.55064583 9.93892956 
+3.75000000 0.93750000 10.04926014 15.54719353 
+
+0.00000000 1.87500000 0.68455136 3.72315860 
+0.93750000 1.87500000 3.18316555 4.94071007 
+1.87500000 1.87500000 5.68177986 7.62183237 
+2.81250000 1.87500000 8.18039417 11.76652527 
+3.75000000 1.87500000 10.67900753 17.37478828 
+
+0.00000000 2.81250000 1.37224269 5.55075455 
+0.93750000 2.81250000 3.87085676 6.76830626 
+1.87500000 2.81250000 6.36947107 9.44942856 
+2.81250000 2.81250000 8.86808491 13.59412098 
+3.75000000 2.81250000 11.36669922 19.20238495 
+
+0.00000000 3.75000000 2.11787748 7.37835026 
+0.93750000 3.75000000 4.61649179 8.59590149 
+1.87500000 3.75000000 7.11510563 11.27702427 
+2.81250000 3.75000000 9.61371994 15.42171669 
+3.75000000 3.75000000 12.11233425 21.02997971 
+
+
+DEAL::scale = 3.00000000
+DEAL::FE_BR<2>(1), testfun(1), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(2), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(3), error_u=7.72593449, error_v=1.09924563
+# This file was generated by the deal.II library.
+
+
+#
+# For a description of the GNUPLOT format see the GNUPLOT manual.
+#
+# <x> <y> <solution_0> <solution_1> 
+0.00000000 0.00000000 -0.53335565 0.06990211 
+1.00000000 0.00000000 2.61032033 0.78492886 
+2.00000000 0.00000000 5.75399637 2.78148818 
+3.00000000 0.00000000 8.89767265 6.05958033 
+4.00000000 0.00000000 12.04134846 10.61920547 
+
+0.00000000 1.00000000 0.93917066 1.17165577 
+1.00000000 1.00000000 4.08284664 1.88668263 
+2.00000000 1.00000000 7.22652245 3.88324189 
+3.00000000 1.00000000 10.37019825 7.16133404 
+4.00000000 1.00000000 13.51387501 11.72095871 
+
+0.00000000 2.00000000 4.40202665 2.27340961 
+1.00000000 2.00000000 7.54570246 2.98843622 
+2.00000000 2.00000000 10.68937874 4.98499584 
+3.00000000 2.00000000 13.83305454 8.26308823 
+4.00000000 2.00000000 16.97673035 12.82271290 
+
+0.00000000 3.00000000 9.85521221 3.37516332 
+1.00000000 3.00000000 12.99888802 4.09018993 
+2.00000000 3.00000000 16.14256477 6.08674955 
+3.00000000 3.00000000 19.28623962 9.36484146 
+4.00000000 3.00000000 22.42991638 13.92446613 
+
+0.00000000 4.00000000 17.29872704 4.47691679 
+1.00000000 4.00000000 20.44240379 5.19194365 
+2.00000000 4.00000000 23.58608055 7.18850327 
+3.00000000 4.00000000 26.72975540 10.46659565 
+4.00000000 4.00000000 29.87343216 15.02622032 
+
+
+DEAL::scale = 3.25000000
+DEAL::FE_BR<2>(1), testfun(1), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(2), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(3), error_u=29.53547728, error_v=2.17221817
+# This file was generated by the deal.II library.
+
+
+#
+# For a description of the GNUPLOT format see the GNUPLOT manual.
+#
+# <x> <y> <solution_0> <solution_1> 
+0.00000000 0.00000000 -2.17405033 0.17477366 
+1.06250000 0.00000000 2.62238026 1.54223979 
+2.12500000 0.00000000 7.41881084 4.67130518 
+3.18750000 0.00000000 12.21524143 9.56196976 
+4.25000000 0.00000000 17.01167297 16.21423340 
+
+0.00000000 1.06250000 -0.14249764 2.29926300 
+1.06250000 1.06250000 4.65393305 3.66672897 
+2.12500000 1.06250000 9.45036316 6.79579449 
+3.18750000 1.06250000 14.24679375 11.68645954 
+4.25000000 1.06250000 19.04322433 18.33872414 
+
+0.00000000 2.12500000 4.07298470 4.42375231 
+1.06250000 2.12500000 8.86941528 5.79121828 
+2.12500000 2.12500000 13.66584587 8.92028332 
+3.18750000 2.12500000 18.46227646 13.81094837 
+4.25000000 2.12500000 23.25870705 20.46321297 
+
+0.00000000 3.18750000 10.47239780 6.54824162 
+1.06250000 3.18750000 15.26882839 7.91570759 
+2.12500000 3.18750000 20.06525803 11.04477310 
+3.18750000 3.18750000 24.86168861 15.93543816 
+4.25000000 3.18750000 29.65811920 22.58770180 
+
+0.00000000 4.25000000 19.05574036 8.67273045 
+1.06250000 4.25000000 23.85217094 10.04019642 
+2.12500000 4.25000000 28.64860153 13.16926193 
+3.18750000 4.25000000 33.44503021 18.05992699 
+4.25000000 4.25000000 38.24146271 24.71219063 
+
+
+DEAL::scale = 3.50000000
+DEAL::FE_BR<2>(1), testfun(1), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(2), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(3), error_u=34.55174478, error_v=14.51208247
+# This file was generated by the deal.II library.
+
+
+#
+# For a description of the GNUPLOT format see the GNUPLOT manual.
+#
+# <x> <y> <solution_0> <solution_1> 
+0.00000000 0.00000000 -2.60036874 -0.65008152 
+1.12500000 0.00000000 2.46324825 0.87296045 
+2.25000000 0.00000000 7.52686548 4.10852957 
+3.37500000 0.00000000 12.59048271 9.05662632 
+4.50000000 0.00000000 17.65409851 15.71724987 
+
+0.00000000 1.12500000 -1.92825568 2.25554991 
+1.12500000 1.12500000 3.13536143 3.77859187 
+2.25000000 1.12500000 8.19897842 7.01416111 
+3.37500000 1.12500000 13.26259518 11.96225739 
+4.50000000 1.12500000 18.32621193 18.62288094 
+
+0.00000000 2.25000000 -0.75241685 5.16118145 
+1.12500000 2.25000000 4.31120014 6.68422318 
+2.25000000 2.25000000 9.37481689 9.91979218 
+3.37500000 2.25000000 14.43843460 14.86788845 
+4.50000000 2.25000000 19.50205040 21.52851295 
+
+0.00000000 3.37500000 0.92714763 8.06681252 
+1.12500000 3.37500000 5.99076462 9.58985424 
+2.25000000 3.37500000 11.05438137 12.82542419 
+3.37500000 3.37500000 16.11799812 17.77351952 
+4.50000000 3.37500000 21.18161583 24.43414307 
+
+0.00000000 4.50000000 3.11043787 10.97244358 
+1.12500000 4.50000000 8.17405510 12.49548626 
+2.25000000 4.50000000 13.23767185 15.73105526 
+3.37500000 4.50000000 18.30128860 20.67915154 
+4.50000000 4.50000000 23.36490631 27.33977509 
+
+
+DEAL::scale = 3.75000000
+DEAL::FE_BR<2>(1), testfun(1), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(2), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(3), error_u=26.05573729, error_v=4.75525127
+# This file was generated by the deal.II library.
+
+
+#
+# For a description of the GNUPLOT format see the GNUPLOT manual.
+#
+# <x> <y> <solution_0> <solution_1> 
+0.00000000 0.00000000 -0.94953853 0.60329670 
+1.18750000 0.00000000 3.59920979 2.30629349 
+2.37500000 0.00000000 8.14795780 6.54596758 
+3.56250000 0.00000000 12.69670677 13.32231903 
+4.75000000 0.00000000 17.24545479 22.63534737 
+
+0.00000000 1.18750000 -0.35205719 2.70813394 
+1.18750000 1.18750000 4.19669104 4.41113091 
+2.37500000 1.18750000 8.74543953 8.65080452 
+3.56250000 1.18750000 13.29418755 15.42715645 
+4.75000000 1.18750000 17.84293556 24.74018478 
+
+0.00000000 2.37500000 1.07146299 4.81297112 
+1.18750000 2.37500000 5.62021160 6.51596785 
+2.37500000 2.37500000 10.16895962 10.75564194 
+3.56250000 2.37500000 14.71770763 17.53199387 
+4.75000000 2.37500000 19.26645660 26.84502220 
+
+0.00000000 3.56250000 3.32102203 6.91780806 
+1.18750000 3.56250000 7.86977053 8.62080479 
+2.37500000 3.56250000 12.41851902 12.86047935 
+3.56250000 3.56250000 16.96726799 19.63683128 
+4.75000000 3.56250000 21.51601601 28.94985962 
+
+0.00000000 4.75000000 6.39661980 9.02264500 
+1.18750000 4.75000000 10.94536781 10.72564220 
+2.37500000 4.75000000 15.49411678 14.96531677 
+3.56250000 4.75000000 20.04286575 21.74166679 
+4.75000000 4.75000000 24.59161377 31.05469704 
+
+
+DEAL::scale = -1.00000000
+DEAL::FE_BR<2>(1), testfun(1), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(2), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(3), error_u=0.00498148, error_v=0.00539865
+# This file was generated by the deal.II library.
+
+
+#
+# For a description of the GNUPLOT format see the GNUPLOT manual.
+#
+# <x> <y> <solution_0> <solution_1> 
+0.00000000 0.00000000 -0.01728528 0.39840850 
+0.25000000 0.00000000 0.27633387 0.61774606 
+0.50000000 0.00000000 0.56995302 0.95148623 
+0.75000000 0.00000000 0.86357212 1.39962888 
+1.00000000 0.00000000 1.15719128 1.96217418 
+
+-0.25000000 0.25000000 0.03271498 0.63627326 
+0.00000000 0.25000000 0.20796853 0.74120826 
+0.25000000 0.25000000 0.38322210 0.96054584 
+0.50000000 0.25000000 0.55847561 1.29428601 
+0.75000000 0.25000000 0.73372918 1.74242866 
+
+-0.50000000 0.50000000 0.21607949 0.87413806 
+-0.25000000 0.50000000 0.27296746 0.86467052 
+0.00000000 0.50000000 0.32985544 0.96960551 
+0.25000000 0.50000000 0.38674340 1.18894303 
+0.50000000 0.50000000 0.44363138 1.52268314 
+
+-0.75000000 0.75000000 0.53280824 1.11200285 
+-0.50000000 0.75000000 0.47133064 0.98813272 
+-0.25000000 0.75000000 0.40985301 0.97866511 
+0.00000000 0.75000000 0.34837541 1.08360016 
+0.25000000 0.75000000 0.28689781 1.30293763 
+
+-1.00000000 1.00000000 0.98290128 1.34986758 
+-0.75000000 1.00000000 0.80305803 1.11159492 
+-0.50000000 1.00000000 0.62321484 0.98772478 
+-0.25000000 1.00000000 0.44337165 0.97825718 
+0.00000000 1.00000000 0.26352847 1.08319223 
+
+
+DEAL::scale = -0.75000000
+DEAL::FE_BR<2>(1), testfun(1), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(2), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(3), error_u=0.00000707, error_v=0.00168315
+# This file was generated by the deal.II library.
+
+
+#
+# For a description of the GNUPLOT format see the GNUPLOT manual.
+#
+# <x> <y> <solution_0> <solution_1> 
+0.00000000 0.00000000 0.87398702 1.25476170 
+0.25000000 0.00000000 1.13239610 1.39224970 
+0.50000000 0.00000000 1.39080513 1.64090562 
+0.75000000 0.00000000 1.64921427 2.00072956 
+1.00000000 0.00000000 1.90762329 2.47172141 
+
+-0.18750000 0.25000000 0.77972025 1.41631019 
+0.06250000 0.25000000 1.03478563 1.47042227 
+0.31250000 0.25000000 1.28985095 1.63570225 
+0.56250000 0.25000000 1.54491627 1.91215014 
+0.81250000 0.25000000 1.79998159 2.29976606 
+
+-0.37500000 0.50000000 0.77068520 1.57785869 
+-0.12500000 0.50000000 1.02240682 1.54859471 
+0.12500000 0.50000000 1.27412844 1.63049877 
+0.37500000 0.50000000 1.52585006 1.82357073 
+0.62500000 0.50000000 1.77757168 2.12781072 
+
+-0.56250000 0.75000000 0.84688193 1.73940718 
+-0.31250000 0.75000000 1.09525979 1.62676728 
+-0.06250000 0.75000000 1.34363770 1.62529540 
+0.18750000 0.75000000 1.59201562 1.73499131 
+0.43750000 0.75000000 1.84039354 1.95585537 
+
+-0.75000000 1.00000000 1.00831044 1.90095556 
+-0.50000000 1.00000000 1.25334454 1.70493984 
+-0.25000000 1.00000000 1.49837875 1.62009192 
+0.00000000 1.00000000 1.74341285 1.64641201 
+0.25000000 1.00000000 1.98844707 1.78390002 
+
+
+DEAL::scale = -0.50000000
+DEAL::FE_BR<2>(1), testfun(1), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(2), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(3), error_u=0.00033116, error_v=0.00040793
+# This file was generated by the deal.II library.
+
+
+#
+# For a description of the GNUPLOT format see the GNUPLOT manual.
+#
+# <x> <y> <solution_0> <solution_1> 
+0.00000000 0.00000000 0.19693322 1.76961040 
+0.25000000 0.00000000 0.29728916 2.00948715 
+0.50000000 0.00000000 0.39764509 2.25636673 
+0.75000000 0.00000000 0.49800101 2.51024914 
+1.00000000 0.00000000 0.59835696 2.77113414 
+
+-0.12500000 0.25000000 0.33199659 1.83642888 
+0.12500000 0.25000000 0.41709322 2.07280421 
+0.37500000 0.25000000 0.50218987 2.31618237 
+0.62500000 0.25000000 0.58728647 2.56656337 
+0.87500000 0.25000000 0.67238313 2.82394719 
+
+-0.25000000 0.50000000 0.48194611 1.90324724 
+0.00000000 0.50000000 0.55178344 2.13612127 
+0.25000000 0.50000000 0.62162083 2.37599802 
+0.50000000 0.50000000 0.69145817 2.62287760 
+0.75000000 0.50000000 0.76129550 2.87676001 
+
+-0.37500000 0.75000000 0.64678180 1.97006571 
+-0.12500000 0.75000000 0.70135987 2.19943833 
+0.12500000 0.75000000 0.75593793 2.43581367 
+0.37500000 0.75000000 0.81051600 2.67919183 
+0.62500000 0.75000000 0.86509407 2.92957282 
+
+-0.50000000 1.00000000 0.82650369 2.03688407 
+-0.25000000 1.00000000 0.86582249 2.26275539 
+0.00000000 1.00000000 0.90514129 2.49562955 
+0.25000000 1.00000000 0.94446003 2.73550630 
+0.50000000 1.00000000 0.98377883 2.98238587 
+
+
+DEAL::scale = -0.25000000
+DEAL::FE_BR<2>(1), testfun(1), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(2), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(3), error_u=0.00482070, error_v=0.00053912
+# This file was generated by the deal.II library.
+
+
+#
+# For a description of the GNUPLOT format see the GNUPLOT manual.
+#
+# <x> <y> <solution_0> <solution_1> 
+0.00000000 0.00000000 0.73046821 0.99419993 
+0.25000000 0.00000000 0.96751040 1.11348605 
+0.50000000 0.00000000 1.20455253 1.31775999 
+0.75000000 0.00000000 1.44159472 1.60702205 
+1.00000000 0.00000000 1.67863691 1.98127198 
+
+-0.06250000 0.25000000 0.81715912 1.16371572 
+0.18750000 0.25000000 1.02509141 1.26175475 
+0.43750000 0.25000000 1.23302352 1.44478178 
+0.68750000 0.25000000 1.44095576 1.71279681 
+0.93750000 0.25000000 1.64888799 2.06579995 
+
+-0.12500000 0.50000000 0.97645611 1.33323145 
+0.12500000 0.50000000 1.15527844 1.41002357 
+0.37500000 0.50000000 1.33410072 1.57180357 
+0.62500000 0.50000000 1.51292300 1.81857169 
+0.87500000 0.50000000 1.69174528 2.15032768 
+
+-0.18750000 0.75000000 1.20835924 1.50274730 
+0.06250000 0.75000000 1.35807157 1.55829239 
+0.31250000 0.75000000 1.50778389 1.69882548 
+0.56250000 0.75000000 1.65749621 1.92434645 
+0.81250000 0.75000000 1.80720854 2.23485541 
+
+-0.25000000 1.00000000 1.51286829 1.67226303 
+0.00000000 1.00000000 1.63347065 1.70656109 
+0.25000000 1.00000000 1.75407314 1.82584727 
+0.50000000 1.00000000 1.87467551 2.03012133 
+0.75000000 1.00000000 1.99527788 2.31938338 
+
+
+DEAL::scale = 0.00000000
+DEAL::FE_BR<2>(1), testfun(1), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(2), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(3), error_u=0.00034781, error_v=0.00301553
+# This file was generated by the deal.II library.
+
+
+#
+# For a description of the GNUPLOT format see the GNUPLOT manual.
+#
+# <x> <y> <solution_0> <solution_1> 
+0.00000000 0.00000000 0.74135637 1.58835232 
+0.25000000 0.00000000 1.01590896 1.77439463 
+0.50000000 0.00000000 1.29046154 2.02681589 
+0.75000000 0.00000000 1.56501412 2.34561658 
+1.00000000 0.00000000 1.83956671 2.73079610 
+
+0.00000000 0.25000000 0.79181415 2.01227832 
+0.25000000 0.25000000 1.06636679 2.19832063 
+0.50000000 0.25000000 1.34091938 2.45074201 
+0.75000000 0.25000000 1.61547196 2.76954246 
+1.00000000 0.25000000 1.89002454 3.15472198 
+
+0.00000000 0.50000000 0.90656972 2.43620420 
+0.25000000 0.50000000 1.18112230 2.62224650 
+0.50000000 0.50000000 1.45567489 2.87466788 
+0.75000000 0.50000000 1.73022747 3.19346833 
+1.00000000 0.50000000 2.00478005 3.57864785 
+
+0.00000000 0.75000000 1.08562303 2.86013031 
+0.25000000 0.75000000 1.36017573 3.04617262 
+0.50000000 0.75000000 1.63472831 3.29859400 
+0.75000000 0.75000000 1.90928090 3.61739445 
+1.00000000 0.75000000 2.18383336 4.00257397 
+
+0.00000000 1.00000000 1.32897425 3.28405619 
+0.25000000 1.00000000 1.60352683 3.47009850 
+0.50000000 1.00000000 1.87807941 3.72251987 
+0.75000000 1.00000000 2.15263200 4.04132032 
+1.00000000 1.00000000 2.42718458 4.42649984 
+
+
+DEAL::scale = 0.25000000
+DEAL::FE_BR<2>(1), testfun(1), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(2), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(3), error_u=0.00473684, error_v=0.00016416
+# This file was generated by the deal.II library.
+
+
+#
+# For a description of the GNUPLOT format see the GNUPLOT manual.
+#
+# <x> <y> <solution_0> <solution_1> 
+0.00000000 0.00000000 0.08048147 1.64427042 
+0.25000000 0.00000000 0.43223876 1.80288434 
+0.50000000 0.00000000 0.78399605 1.97310567 
+0.75000000 0.00000000 1.13575327 2.15493417 
+1.00000000 0.00000000 1.48751056 2.34837008 
+
+0.06250000 0.25000000 0.15072283 1.94231474 
+0.31250000 0.25000000 0.53133577 2.10383058 
+0.56250000 0.25000000 0.91194868 2.27695346 
+0.81250000 0.25000000 1.29256165 2.46168399 
+1.06250000 0.25000000 1.67317450 2.65802169 
+
+0.12500000 0.50000000 0.25878540 2.24035907 
+0.37500000 0.50000000 0.66825396 2.40477657 
+0.62500000 0.50000000 1.07772255 2.58080149 
+0.87500000 0.50000000 1.48719108 2.76843357 
+1.12500000 0.50000000 1.89665973 2.96767306 
+
+0.18750000 0.75000000 0.40466917 2.53840327 
+0.43750000 0.75000000 0.84299338 2.70572257 
+0.68750000 0.75000000 1.28131759 2.88464928 
+0.93750000 0.75000000 1.71964180 3.07518339 
+1.18750000 0.75000000 2.15796614 3.27732468 
+
+0.25000000 1.00000000 0.58837414 2.83644748 
+0.50000000 1.00000000 1.05555403 3.00666881 
+0.75000000 1.00000000 1.52273393 3.18849730 
+1.00000000 1.00000000 1.98991382 3.38193321 
+1.25000000 1.00000000 2.45709372 3.58697629 
+
+
+DEAL::scale = 0.50000000
+DEAL::FE_BR<2>(1), testfun(1), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(2), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(3), error_u=0.00364269, error_v=0.00595687
+# This file was generated by the deal.II library.
+
+
+#
+# For a description of the GNUPLOT format see the GNUPLOT manual.
+#
+# <x> <y> <solution_0> <solution_1> 
+0.00000000 0.00000000 0.23498216 0.09740061 
+0.25000000 0.00000000 0.49724805 0.37938294 
+0.50000000 0.00000000 0.75951391 0.75647306 
+0.75000000 0.00000000 1.02177978 1.22867084 
+1.00000000 0.00000000 1.28404570 1.79597652 
+
+0.12500000 0.25000000 0.48155794 0.71876413 
+0.37500000 0.25000000 0.79443276 1.04830039 
+0.62500000 0.25000000 1.10730755 1.47294426 
+0.87500000 0.25000000 1.42018235 1.99269605 
+1.12500000 0.25000000 1.73305714 2.60755539 
+
+0.25000000 0.50000000 0.78808987 1.34012759 
+0.50000000 0.50000000 1.15157354 1.71721768 
+0.75000000 0.50000000 1.51505733 2.18941545 
+1.00000000 0.50000000 1.87854111 2.75672126 
+1.25000000 0.50000000 2.24202490 3.41913438 
+
+0.37500000 0.75000000 1.15457797 1.96149111 
+0.62500000 0.75000000 1.56867063 2.38613510 
+0.87500000 0.75000000 1.98276329 2.90588689 
+1.12500000 0.75000000 2.39685583 3.52074623 
+1.37500000 0.75000000 2.81094861 4.23071337 
+
+0.50000000 1.00000000 1.58102226 2.58285451 
+0.75000000 1.00000000 2.04572392 3.05505252 
+1.00000000 1.00000000 2.51042533 3.62235808 
+1.25000000 1.00000000 2.97512698 4.28477144 
+1.50000000 1.00000000 3.43982863 5.04229259 
+
+
+DEAL::scale = 0.75000000
+DEAL::FE_BR<2>(1), testfun(1), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(2), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(3), error_u=0.00188471, error_v=0.00498282
+# This file was generated by the deal.II library.
+
+
+#
+# For a description of the GNUPLOT format see the GNUPLOT manual.
+#
+# <x> <y> <solution_0> <solution_1> 
+0.00000000 0.00000000 0.22824724 0.27658778 
+0.25000000 0.00000000 0.59403044 0.56040615 
+0.50000000 0.00000000 0.95981365 0.94025022 
+0.75000000 0.00000000 1.32559681 1.41612005 
+1.00000000 0.00000000 1.69138002 1.98801553 
+
+0.18750000 0.25000000 0.61398876 0.69977105 
+0.43750000 0.25000000 1.03437662 1.05560875 
+0.68750000 0.25000000 1.45476449 1.50747204 
+0.93750000 0.25000000 1.87515235 2.05536103 
+1.18750000 0.25000000 2.29554009 2.69927597 
+
+0.37500000 0.50000000 1.10679436 1.12295425 
+0.62500000 0.50000000 1.58178687 1.55081117 
+0.87500000 0.50000000 2.05677938 2.07469392 
+1.12500000 0.50000000 2.53177190 2.69460225 
+1.37500000 0.50000000 3.00676441 3.41053629 
+
+0.56250000 0.75000000 1.70666409 1.54613757 
+0.81250000 0.75000000 2.23626137 2.04601383 
+1.06250000 0.75000000 2.76585841 2.64191556 
+1.31250000 0.75000000 3.29545569 3.33384323 
+1.56250000 0.75000000 3.82505274 4.12179661 
+
+0.75000000 1.00000000 2.41359782 1.96932077 
+1.00000000 1.00000000 2.99779963 2.54121637 
+1.25000000 1.00000000 3.58200145 3.20913744 
+1.50000000 1.00000000 4.16620350 3.97308445 
+1.75000000 1.00000000 4.75040531 4.83305693 
+
+
+DEAL::Arbitrary
+
+DEAL::FE_BR<2>(1), testfun(1), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(2), error_u=0.00000000, error_v=0.00000000
+DEAL::FE_BR<2>(1), testfun(3), error_u=0.00076849, error_v=0.00050338
+# This file was generated by the deal.II library.
+
+
+#
+# For a description of the GNUPLOT format see the GNUPLOT manual.
+#
+# <x> <y> <solution_0> <solution_1> 
+-0.03524503 -0.10095209 1.39511764 0.97101939 
+0.21942309 -0.10544990 1.51506829 1.10695076 
+0.47409120 -0.10994771 1.63501894 1.34926820 
+0.72875935 -0.11444552 1.75496960 1.69797182 
+0.98342746 -0.11894333 1.87492025 2.15306139 
+
+-0.04321218 0.16848980 1.58335984 1.26853192 
+0.20366490 0.16984205 1.69842768 1.40314412 
+0.45054197 0.17119431 1.81349564 1.63804901 
+0.69741905 0.17254657 1.92856348 1.97324669 
+0.94429612 0.17389882 2.04363132 2.40873718 
+
+-0.05117932 0.43793169 1.87308323 1.56604445 
+0.18790671 0.44513401 1.98816168 1.69933736 
+0.42699274 0.45233634 2.10324001 1.92682981 
+0.66607881 0.45953864 2.21831846 2.24852157 
+0.90516484 0.46674097 2.33339691 2.66441298 
+
+-0.05914646 0.70737356 2.26428771 1.86355710 
+0.17214854 0.72042596 2.38427019 1.99553072 
+0.40344352 0.73347837 2.50425243 2.21561050 
+0.63473850 0.74653077 2.62423491 2.52379656 
+0.86603349 0.75958312 2.74421716 2.92008877 
+
+-0.06711360 0.97681546 2.75697351 2.16106963 
+0.15639035 0.99571788 2.88675332 2.29172397 
+0.37989432 1.01462042 3.01653290 2.50439143 
+0.60339826 1.03352284 3.14631248 2.79907155 
+0.82690221 1.05242527 3.27609205 3.17576480 
+
+

diff --git a/tests/fe/fe_br.cc b/tests/fe/fe_br.cc
new file mode 100644 (file)
index 0000000..d54e39c
--- /dev/null
+++ b/tests/fe/fe_br.cc
@@ -0,0 +1,141 @@
+// ---------------------------------------------------------------------
+//
+//
+//
+//
+//
+//
+//
+//
+//
+//
+//
+//
+// ---------------------------------------------------------------------
+
+
+// check the correctness of fe_values.shape_gradient for FE_BernardiRaugel
+// this test is almost a verbatim copy of the fe_rt.cc file
+
+#include <deal.II/base/function.h>
+#include <deal.II/base/quadrature_lib.h>
+
+#include <deal.II/dofs/dof_handler.h>
+
+#include <deal.II/fe/fe_bernardi_raugel.h>
+#include <deal.II/fe/fe_dgq.h>
+#include <deal.II/fe/fe_nedelec.h>
+#include <deal.II/fe/fe_q.h>
+#include <deal.II/fe/fe_system.h>
+#include <deal.II/fe/fe_values.h>
+#include <deal.II/fe/mapping_q1.h>
+
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/tria_boundary_lib.h>
+
+#include <deal.II/lac/vector.h>
+
+#include <sstream>
+
+#include "../tests.h"
+
+
+
+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(4);
+  FEValues<dim>     fe_values(fe,
+                          quadrature,
+                          update_gradients | update_quadrature_points |
+                            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;
+        }
+
+      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<1, dim> bulk_integral;
+              for (unsigned int q = 0; q < fe_values.n_quadrature_points; ++q)
+                {
+                  bulk_integral += fe_values[single_component].gradient(i, q) *
+                                   fe_values.JxW(q);
+                }
+
+              deallog << "    bulk integral=" << bulk_integral << std::endl;
+            }
+        }
+    }
+}
+
+
+
+template <int dim>
+void
+test_hyper_cube(const double tolerance)
+{
+  Triangulation<dim> tr;
+  GridGenerator::hyper_cube(tr);
+
+  typename Triangulation<dim>::active_cell_iterator cell = tr.begin_active();
+  for (unsigned int i = 0; i < GeometryInfo<dim>::vertices_per_cell; ++i)
+    {
+      Point<dim> &point = cell->vertex(i);
+      if (std::abs(point(dim - 1) - 1.0) < 1e-5)
+        point(dim - 1) += 0.15;
+    }
+
+  FE_BernardiRaugel<dim> fe(1);
+  test(tr, fe, tolerance);
+}
+
+
+int
+main()
+{
+  std::ofstream logfile("output");
+  deallog << std::setprecision(3);
+
+  deallog.attach(logfile);
+
+  test_hyper_cube<2>(1e-6);
+  test_hyper_cube<3>(1e-6);
+}

diff --git a/tests/fe/fe_br.output b/tests/fe/fe_br.output
new file mode 100644 (file)
index 0000000..31a038b
--- /dev/null
+++ b/tests/fe/fe_br.output
@@ -0,0 +1,131 @@
+
+DEAL::FE=FE_BR<2>(1)
+DEAL::Cell nodes:
+DEAL::0: ( 0.00 0.00 )
+DEAL::1: ( 1.00 0.00 )
+DEAL::2: ( 0.00 1.15 )
+DEAL::3: ( 1.00 1.15 )
+DEAL::    bulk integral=-0.575 -0.500
+DEAL::    bulk integral=0.00 0.00
+DEAL::    bulk integral=0.575 -0.500
+DEAL::    bulk integral=0.00 0.00
+DEAL::    bulk integral=-0.575 0.500
+DEAL::    bulk integral=0.00 0.00
+DEAL::    bulk integral=0.575 0.500
+DEAL::    bulk integral=0.00 0.00
+DEAL::    bulk integral=-0.767 -1.99e-17
+DEAL::    bulk integral=0.767 -2.78e-17
+DEAL::    bulk integral=0.00 0.00
+DEAL::    bulk integral=0.00 0.00
+DEAL::    bulk integral=0.00 0.00
+DEAL::    bulk integral=-0.575 -0.500
+DEAL::    bulk integral=0.00 0.00
+DEAL::    bulk integral=0.575 -0.500
+DEAL::    bulk integral=0.00 0.00
+DEAL::    bulk integral=-0.575 0.500
+DEAL::    bulk integral=0.00 0.00
+DEAL::    bulk integral=0.575 0.500
+DEAL::    bulk integral=0.00 0.00
+DEAL::    bulk integral=0.00 0.00
+DEAL::    bulk integral=1.21e-17 -0.667
+DEAL::    bulk integral=-2.78e-17 0.667
+DEAL::FE=FE_BR<3>(1)
+DEAL::Cell nodes:
+DEAL::0: ( 0.00 0.00 0.00 )
+DEAL::1: ( 1.00 0.00 0.00 )
+DEAL::2: ( 0.00 1.00 0.00 )
+DEAL::3: ( 1.00 1.00 0.00 )
+DEAL::4: ( 0.00 0.00 1.15 )
+DEAL::5: ( 1.00 0.00 1.15 )
+DEAL::6: ( 0.00 1.00 1.15 )
+DEAL::7: ( 1.00 1.00 1.15 )
+DEAL::    bulk integral=-0.287 -0.287 -0.250
+DEAL::    bulk integral=0.00 0.00 0.00
+DEAL::    bulk integral=0.00 0.00 0.00
+DEAL::    bulk integral=0.287 -0.287 -0.250
+DEAL::    bulk integral=0.00 0.00 0.00
+DEAL::    bulk integral=0.00 0.00 0.00
+DEAL::    bulk integral=-0.287 0.287 -0.250
+DEAL::    bulk integral=0.00 0.00 0.00
+DEAL::    bulk integral=0.00 0.00 0.00
+DEAL::    bulk integral=0.287 0.287 -0.250
+DEAL::    bulk integral=0.00 0.00 0.00
+DEAL::    bulk integral=0.00 0.00 0.00
+DEAL::    bulk integral=-0.287 -0.287 0.250
+DEAL::    bulk integral=0.00 0.00 0.00
+DEAL::    bulk integral=0.00 0.00 0.00
+DEAL::    bulk integral=0.287 -0.287 0.250
+DEAL::    bulk integral=0.00 0.00 0.00
+DEAL::    bulk integral=0.00 0.00 0.00
+DEAL::    bulk integral=-0.287 0.287 0.250
+DEAL::    bulk integral=0.00 0.00 0.00
+DEAL::    bulk integral=0.00 0.00 0.00
+DEAL::    bulk integral=0.287 0.287 0.250
+DEAL::    bulk integral=0.00 0.00 0.00
+DEAL::    bulk integral=0.00 0.00 0.00
+DEAL::    bulk integral=-0.511 1.04e-17 -5.81e-17
+DEAL::    bulk integral=0.511 1.21e-17 3.04e-17
+DEAL::    bulk integral=0.00 0.00 0.00
+DEAL::    bulk integral=0.00 0.00 0.00
+DEAL::    bulk integral=0.00 0.00 0.00
+DEAL::    bulk integral=0.00 0.00 0.00
+DEAL::    bulk integral=0.00 0.00 0.00
+DEAL::    bulk integral=-0.287 -0.287 -0.250
+DEAL::    bulk integral=0.00 0.00 0.00
+DEAL::    bulk integral=0.00 0.00 0.00
+DEAL::    bulk integral=0.287 -0.287 -0.250
+DEAL::    bulk integral=0.00 0.00 0.00
+DEAL::    bulk integral=0.00 0.00 0.00
+DEAL::    bulk integral=-0.287 0.287 -0.250
+DEAL::    bulk integral=0.00 0.00 0.00
+DEAL::    bulk integral=0.00 0.00 0.00
+DEAL::    bulk integral=0.287 0.287 -0.250
+DEAL::    bulk integral=0.00 0.00 0.00
+DEAL::    bulk integral=0.00 0.00 0.00
+DEAL::    bulk integral=-0.287 -0.287 0.250
+DEAL::    bulk integral=0.00 0.00 0.00
+DEAL::    bulk integral=0.00 0.00 0.00
+DEAL::    bulk integral=0.287 -0.287 0.250
+DEAL::    bulk integral=0.00 0.00 0.00
+DEAL::    bulk integral=0.00 0.00 0.00
+DEAL::    bulk integral=-0.287 0.287 0.250
+DEAL::    bulk integral=0.00 0.00 0.00
+DEAL::    bulk integral=0.00 0.00 0.00
+DEAL::    bulk integral=0.287 0.287 0.250
+DEAL::    bulk integral=0.00 0.00 0.00
+DEAL::    bulk integral=0.00 0.00 0.00
+DEAL::    bulk integral=0.00 0.00 0.00
+DEAL::    bulk integral=-4.77e-18 -0.511 4.94e-17
+DEAL::    bulk integral=-6.94e-18 0.511 1.30e-17
+DEAL::    bulk integral=0.00 0.00 0.00
+DEAL::    bulk integral=0.00 0.00 0.00
+DEAL::    bulk integral=0.00 0.00 0.00
+DEAL::    bulk integral=0.00 0.00 0.00
+DEAL::    bulk integral=-0.287 -0.287 -0.250
+DEAL::    bulk integral=0.00 0.00 0.00
+DEAL::    bulk integral=0.00 0.00 0.00
+DEAL::    bulk integral=0.287 -0.287 -0.250
+DEAL::    bulk integral=0.00 0.00 0.00
+DEAL::    bulk integral=0.00 0.00 0.00
+DEAL::    bulk integral=-0.287 0.287 -0.250
+DEAL::    bulk integral=0.00 0.00 0.00
+DEAL::    bulk integral=0.00 0.00 0.00
+DEAL::    bulk integral=0.287 0.287 -0.250
+DEAL::    bulk integral=0.00 0.00 0.00
+DEAL::    bulk integral=0.00 0.00 0.00
+DEAL::    bulk integral=-0.287 -0.287 0.250
+DEAL::    bulk integral=0.00 0.00 0.00
+DEAL::    bulk integral=0.00 0.00 0.00
+DEAL::    bulk integral=0.287 -0.287 0.250
+DEAL::    bulk integral=0.00 0.00 0.00
+DEAL::    bulk integral=0.00 0.00 0.00
+DEAL::    bulk integral=-0.287 0.287 0.250
+DEAL::    bulk integral=0.00 0.00 0.00
+DEAL::    bulk integral=0.00 0.00 0.00
+DEAL::    bulk integral=0.287 0.287 0.250
+DEAL::    bulk integral=0.00 0.00 0.00
+DEAL::    bulk integral=0.00 0.00 0.00
+DEAL::    bulk integral=0.00 0.00 0.00
+DEAL::    bulk integral=0.00 0.00 0.00
+DEAL::    bulk integral=-6.88e-18 1.08e-17 -0.444
+DEAL::    bulk integral=-6.07e-18 3.38e-17 0.444