Lowest order Rannacher Turek polynomials and FE in 2D and tests.
(Jason Sheldon, Wolfgang Bangerth, 2015/08/13)
</li>
+ <li> New: FE_RannacherTurek describes a discontinuous FiniteElement
+ with vanishing mean values of jumps across faces.
+ <br>
+ (Patrick Esser, 2015/08/17)
+ </li>
+
<li> New: FE_Q_Bubbles describes a FiniteElement based on FE_Q
enriched by bubble functions.
<br>
--- /dev/null
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 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.
+//
+// ---------------------------------------------------------------------
+
+
+#ifndef dealii__polynomials_rannacher_turek_h
+#define dealii__polynomials_rannacher_turek_h
+
+#include <deal.II/base/point.h>
+#include <deal.II/base/tensor.h>
+#include <vector>
+
+DEAL_II_NAMESPACE_OPEN
+
+
+/**
+ * Basis for polynomial space on the unit square used for lowest order
+ * Rannacher Turek element.
+ *
+ * The i-th basis function is the dual basis element corresponding to
+ * the dof which evaluates the function's mean value across the i-th
+ * face. The numbering can be found in GeometryInfo.
+ *
+ * @ingroup Polynomials
+ * @author Patrick Esser
+ * @date 2015
+ **/
+template <int dim>
+class PolynomialsRannacherTurek
+{
+public:
+ /**
+ * Dimension we are working in.
+ */
+ static const unsigned int dimension = dim;
+
+ /**
+ * Constructor, checking that the basis is implemented in this
+ * dimension.
+ */
+ PolynomialsRannacherTurek();
+
+ /** Value of basis function @p i at @p p.
+ */
+ double compute_value(const unsigned int i,
+ const Point<dim> &p) const;
+ /** Gradient of basis function @p i at @p p.
+ */
+ Tensor<1, dim> compute_grad(const unsigned int i,
+ const Point<dim> &p) const;
+ /** Gradient of gradient of basis function @p i at @p p.
+ */
+ Tensor<2, dim> compute_grad_grad(const unsigned int i,
+ const Point<dim> &p) const;
+
+ /**
+ * Compute values and derivatives of all basis functions at @p
+ * unit_point.
+ *
+ * Size of the vectors must be either equal to the number of
+ * polynomials or zero. A size of zero means that we are not
+ * computing the vector entries.
+ */
+ void compute(const Point<dim> &unit_point,
+ std::vector<double> &values,
+ std::vector<Tensor<1, dim> > &grads,
+ std::vector<Tensor<2, dim> > &grad_grads) const;
+};
+
+
+DEAL_II_NAMESPACE_CLOSE
+
+#endif
--- /dev/null
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 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.
+//
+// ---------------------------------------------------------------------
+
+
+#ifndef dealii__fe_rannacher_turek_h
+#define dealii__fe_rannacher_turek_h
+
+#include <deal.II/base/polynomials_rannacher_turek.h>
+#include <deal.II/fe/fe_poly.h>
+#include <deal.II/fe/fe_base.h>
+#include <string>
+#include <vector>
+
+DEAL_II_NAMESPACE_OPEN
+
+
+/**
+ * Implementation of Rannacher-Turek elements. Functions generated by this
+ * element will be discontinuous, but their jump along faces is mean value
+ * free.
+ *
+ * Implemented only in dimension 2, lowest order, without hanging nodes and
+ * restriction/prolongation.
+ *
+ * <h3>Interpolation</h3>
+ *
+ * <h4>Node values</h4>
+ * The @ref GlossNodes "node values" are moments on faces.
+ *
+ * <h4>Generalized support points</h4>
+ * To calculate the node values, we are using a QGauss rule on each face.
+ * By default, we are using a two point rule to integrate Rannacher-Turek
+ * functions exactly. But in order to be able to interpolate other
+ * functions with sufficient accuracy, the number of quadrature points
+ * used on a face can be adjusted in the constructor.
+ *
+ * @ingroup fe
+ * @author Patrick Esser
+ * @date 2015
+ */
+template <int dim>
+class FE_RannacherTurek : public FE_Poly<PolynomialsRannacherTurek<dim>, dim>
+{
+public:
+ /**
+ * Constructor for Rannacher-Turek element of degree @p degree, using
+ * @p n_face_support_points quadrature points on each face for
+ * interpolation. Notice that the element of degree 0 contains
+ * polynomials of degree 2.
+ *
+ * Only implemented for degree 0 in 2D.
+ */
+ FE_RannacherTurek(const unsigned int degree = 0,
+ const unsigned int n_face_support_points = 2);
+
+ virtual std::string get_name() const;
+ virtual FiniteElement<dim> *clone() const;
+
+ virtual void interpolate(
+ std::vector<double> &local_dofs,
+ const std::vector<double> &values) const;
+private:
+ /**
+ * Degree of this element.
+ */
+ const unsigned int degree;
+ /**
+ * The number of quadrature points used on each face to evaluate node
+ * functionals during interpolation.
+ */
+ const unsigned int n_face_support_points;
+ /**
+ * The weights used on the faces to evaluate node functionals.
+ */
+ std::vector<double> weights;
+
+ /**
+ * Compute generalized support points and their weights.
+ */
+ void initialize_support_points();
+ /**
+ * Return information about degrees of freedom per object as needed
+ * during construction.
+ */
+ std::vector<unsigned int> get_dpo_vector();
+};
+
+
+DEAL_II_NAMESPACE_CLOSE
+
+#endif
polynomial_space.cc
polynomials_p.cc
polynomials_piecewise.cc
+ polynomials_rannacher_turek.cc
polynomials_raviart_thomas.cc
quadrature.cc
quadrature_lib.cc
SET(_inst
data_out_base.inst.in
+ polynomials_rannacher_turek.inst.in
time_stepping.inst.in
)
--- /dev/null
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 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.
+//
+// ---------------------------------------------------------------------
+
+
+#include <deal.II/base/polynomials_rannacher_turek.h>
+#include <deal.II/base/geometry_info.h>
+
+DEAL_II_NAMESPACE_OPEN
+
+
+template <int dim>
+PolynomialsRannacherTurek<dim>::PolynomialsRannacherTurek()
+{
+ Assert(dim == 2, ExcNotImplemented());
+}
+
+
+
+template <int dim>
+double PolynomialsRannacherTurek<dim>::compute_value(const unsigned int i,
+ const Point<dim> &p) const
+{
+ Assert(dim == 2, ExcNotImplemented());
+ if (i == 0)
+ {
+ return (0.75 - 2.5*p(0) + 1.5*p(1) + 1.5*(p(0)*p(0) - p(1)*p(1)));
+ }
+ else if (i == 1)
+ {
+ return (-0.25 - 0.5*p(0) + 1.5*p(1) + 1.5*(p(0)*p(0) - p(1)*p(1)));
+ }
+ else if (i == 2)
+ {
+ return (0.75 + 1.5*p(0) - 2.5*p(1) - 1.5*(p(0)*p(0) - p(1)*p(1)));
+ }
+ else if (i == 3)
+ {
+ return (-0.25 + 1.5*p(0) - 0.5*p(1) - 1.5*(p(0)*p(0) - p(1)*p(1)));
+ }
+
+ Assert(false, ExcNotImplemented());
+ return 0;
+}
+
+
+
+template <int dim>
+Tensor<1, dim> PolynomialsRannacherTurek<dim>::compute_grad(
+ const unsigned int i,
+ const Point<dim> &p) const
+{
+ Assert(dim == 2, ExcNotImplemented());
+ Tensor<1, dim> grad;
+ if (i == 0)
+ {
+ grad[0] = -2.5 + 3*p(0);
+ grad[1] = 1.5 - 3*p(1);
+ }
+ else if (i == 1)
+ {
+ grad[0] = -0.5 + 3.0*p(0);
+ grad[1] = 1.5 - 3.0*p(1);
+ }
+ else if (i == 2)
+ {
+ grad[0] = 1.5 - 3.0*p(0);
+ grad[1] = -2.5 + 3.0*p(1);
+ }
+ else if (i == 3)
+ {
+ grad[0] = 1.5 - 3.0*p(0);
+ grad[1] = -0.5 + 3.0*p(1);
+ }
+ else
+ {
+ Assert(false, ExcNotImplemented());
+ }
+
+ return grad;
+}
+
+
+
+template <int dim> Tensor<2, dim>
+PolynomialsRannacherTurek<dim>::compute_grad_grad(const unsigned int i,
+ const Point<dim> & /*p*/)
+const
+{
+ Assert(dim == 2, ExcNotImplemented());
+ Tensor<2, dim> grad_grad;
+ if (i == 0)
+ {
+ grad_grad[0][0] = 3;
+ grad_grad[0][1] = 0;
+ grad_grad[1][0] = 0;
+ grad_grad[1][1] = -3;
+ }
+ else if (i == 1)
+ {
+ grad_grad[0][0] = 3;
+ grad_grad[0][1] = 0;
+ grad_grad[1][0] = 0;
+ grad_grad[1][1] = -3;
+ }
+ else if (i == 2)
+ {
+ grad_grad[0][0] = -3;
+ grad_grad[0][1] = 0;
+ grad_grad[1][0] = 0;
+ grad_grad[1][1] = 3;
+ }
+ else if (i == 3)
+ {
+ grad_grad[0][0] = -3;
+ grad_grad[0][1] = 0;
+ grad_grad[1][0] = 0;
+ grad_grad[1][1] = 3;
+ }
+ return grad_grad;
+}
+
+
+
+template <int dim>
+void PolynomialsRannacherTurek<dim>::compute(
+ const Point<dim> &unit_point,
+ std::vector<double> &values,
+ std::vector<Tensor<1, dim> > &grads,
+ std::vector<Tensor<2, dim> > &grad_grads) const
+{
+ const unsigned int n_pols = dealii::GeometryInfo<dim>::faces_per_cell;
+ Assert(values.size() == n_pols || values.size() == 0,
+ ExcDimensionMismatch(values.size(), n_pols));
+ Assert(grads.size() == n_pols || grads.size() == 0,
+ ExcDimensionMismatch(grads.size(), n_pols));
+ Assert(grad_grads.size() == n_pols || grad_grads.size() == 0,
+ ExcDimensionMismatch(grad_grads.size(), n_pols));
+
+ for (unsigned int i = 0; i < n_pols; ++i)
+ {
+ if (values.size() != 0)
+ {
+ values[i] = compute_value(i, unit_point);
+ }
+ if (grads.size() != 0)
+ {
+ grads[i] = compute_grad(i, unit_point);
+ }
+ if (grad_grads.size() != 0)
+ {
+ grad_grads[i] = compute_grad_grad(i, unit_point);
+ }
+ }
+}
+
+
+// explicit instantiations
+#include "polynomials_rannacher_turek.inst"
+
+DEAL_II_NAMESPACE_CLOSE
--- /dev/null
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 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.
+//
+// ---------------------------------------------------------------------
+
+
+
+for (deal_II_dimension : DIMENSIONS)
+ {
+ template class PolynomialsRannacherTurek<deal_II_dimension>;
+ }
+
fe_q_dg0.cc
fe_q_hierarchical.cc
fe_q_iso_q1.cc
+ fe_rannacher_turek.cc
fe_raviart_thomas.cc
fe_raviart_thomas_nodal.cc
fe_system.cc
fe_q_hierarchical.inst.in
fe_q.inst.in
fe_q_iso_q1.inst.in
+ fe_rannacher_turek.inst.in
fe_raviart_thomas.inst.in
fe_raviart_thomas_nodal.inst.in
fe_system.inst.in
#include <deal.II/base/tensor_product_polynomials_bubbles.h>
#include <deal.II/base/polynomials_p.h>
#include <deal.II/base/polynomials_piecewise.h>
+#include <deal.II/base/polynomials_rannacher_turek.h>
#include <deal.II/fe/fe_poly.h>
#include <deal.II/fe/fe_values.h>
#include <deal.II/fe/fe_poly.templates.h>
template class FE_Poly<TensorProductPolynomials<deal_II_dimension,Polynomials::PiecewisePolynomial<double> >, deal_II_dimension, deal_II_space_dimension>;
template class FE_Poly<PolynomialSpace<deal_II_dimension>, deal_II_dimension, deal_II_space_dimension>;
template class FE_Poly<PolynomialsP<deal_II_dimension>, deal_II_dimension, deal_II_space_dimension>;
+ template class FE_Poly<PolynomialsRannacherTurek<deal_II_dimension>, deal_II_dimension, deal_II_space_dimension>;
#endif
}
--- /dev/null
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 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.
+//
+// ---------------------------------------------------------------------
+
+
+#include <deal.II/fe/fe_rannacher_turek.h>
+#include <deal.II/base/quadrature_lib.h>
+#include <algorithm>
+
+#include <sstream>
+
+
+DEAL_II_NAMESPACE_OPEN
+
+
+template <int dim>
+FE_RannacherTurek<dim>::FE_RannacherTurek(const unsigned int degree,
+ const unsigned int n_face_support_points) :
+ FE_Poly<PolynomialsRannacherTurek<dim>, dim>(
+ PolynomialsRannacherTurek<dim>(),
+ FiniteElementData<dim>(this->get_dpo_vector(),
+ 1,
+ 2,
+ FiniteElementData<dim>::L2),
+ std::vector<bool>(4, false), // restriction not implemented
+ std::vector<ComponentMask>(4, std::vector<bool>(1, true))),
+ degree(degree),
+ n_face_support_points(n_face_support_points)
+{
+ Assert(dim == 2, ExcNotImplemented());
+ Assert(degree == 0, ExcNotImplemented());
+ this->initialize_support_points();
+}
+
+
+
+template <int dim>
+std::vector<unsigned int> FE_RannacherTurek<dim>::get_dpo_vector()
+{
+ std::vector<unsigned int> dpo(dim + 1, 0);
+ dpo[dim - 1] = 1;
+
+ return dpo;
+}
+
+
+
+template <int dim>
+std::string FE_RannacherTurek<dim>::get_name() const
+{
+ std::ostringstream namebuf;
+ namebuf << "FE_RannacherTurek"
+ << "<" << dim << ">"
+ << "(" << this->degree << ", " << this-n_face_support_points << ")";
+ return namebuf.str();
+}
+
+
+
+template <int dim>
+FiniteElement<dim> *FE_RannacherTurek<dim>::clone() const
+{
+ return new FE_RannacherTurek<dim>(this->degree, this->n_face_support_points);
+}
+
+
+
+template <int dim>
+void FE_RannacherTurek<dim>::initialize_support_points()
+{
+ Assert(dim == 2, ExcNotImplemented());
+ dealii::QGauss<dim-1> face_quadrature(this->n_face_support_points);
+ this->weights = face_quadrature.get_weights();
+ this->generalized_support_points.resize(4*face_quadrature.size());
+ for (unsigned int q = 0;
+ q < face_quadrature.size();
+ ++q)
+ {
+ this->generalized_support_points[0*face_quadrature.size() + q] =
+ dealii::Point<dim>(0, 1 - face_quadrature.point(q)(0));
+ this->generalized_support_points[1*face_quadrature.size() + q] =
+ dealii::Point<dim>(1, 1 - face_quadrature.point(q)(0));
+ this->generalized_support_points[2*face_quadrature.size() + q] =
+ dealii::Point<dim>(face_quadrature.point(q)(0), 0);
+ this->generalized_support_points[3*face_quadrature.size() + q] =
+ dealii::Point<dim>(face_quadrature.point(q)(0), 1);
+ }
+}
+
+
+
+template <int dim>
+void FE_RannacherTurek<dim>::interpolate(
+ std::vector<double> &local_dofs,
+ const std::vector<double> &values) const
+{
+ AssertDimension(values.size(), this->generalized_support_points.size());
+ AssertDimension(local_dofs.size(), this->dofs_per_cell);
+
+ const unsigned int q_points_per_face = this->weights.size();
+ std::fill(local_dofs.begin(), local_dofs.end(), 0.0);
+
+ std::vector<double>::const_iterator value = values.begin();
+ for (unsigned int face = 0;
+ face < dealii::GeometryInfo<dim>::faces_per_cell;
+ ++face)
+ {
+ for (unsigned int q = 0;
+ q < q_points_per_face;
+ ++q)
+ {
+ local_dofs[face] += (*value) * this->weights[q];
+ ++value;
+ }
+ }
+}
+
+
+
+// explicit instantiations
+#include "fe_rannacher_turek.inst"
+
+DEAL_II_NAMESPACE_CLOSE
--- /dev/null
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 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.
+//
+// ---------------------------------------------------------------------
+
+
+
+for (deal_II_dimension : DIMENSIONS)
+ {
+ template class FE_RannacherTurek<deal_II_dimension>;
+ }
+
--- /dev/null
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 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.
+//
+// ---------------------------------------------------------------------
+
+
+// Interfaces being tested
+#include <deal.II/fe/fe_rannacher_turek.h>
+#include <deal.II/base/polynomials_rannacher_turek.h>
+// Interfaces needed for testing
+#include <deal.II/grid/tria.h>
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/dofs/dof_handler.h>
+#include <deal.II/fe/fe_values.h>
+#include <deal.II/base/quadrature_lib.h>
+
+#include "../tests.h"
+
+// Known results for the Rannacher Turek element. All output should be zero.
+
+void test_known_values()
+{
+ PolynomialsRannacherTurek<2> pols;
+ Point<2> p(0.5, 0.5);
+ for (unsigned int i = 0; i < 4; ++i)
+ {
+ deallog << pols.compute_value(i, p) - 0.25 << std::endl;
+ }
+}
+
+void test_n_dofs()
+{
+ FE_RannacherTurek<2> fe_ratu;
+
+ Triangulation<2> tria;
+ GridGenerator::hyper_cube(tria, -1, 1);
+ tria.refine_global(1);
+
+ DoFHandler<2> dofh;
+ dofh.initialize(tria, fe_ratu);
+
+ deallog << dofh.n_dofs() - 12 << std::endl;
+}
+
+void test_nodal_matrix()
+{
+ FE_RannacherTurek<2> fe;
+
+ FullMatrix<double> N(4, 4);
+ // compute_node_matrix does not check for number of components but
+ // simply assumes that there are dim components. Thus we do it ourselves.
+ const unsigned int n_dofs = fe.dofs_per_cell;
+ const std::vector<Point<2> > &points = fe.get_generalized_support_points();
+ std::vector<double> values(points.size());
+ std::vector<double> local_dofs(n_dofs);
+
+ for (unsigned int i = 0; i < n_dofs; ++i)
+ {
+ for (unsigned int k = 0; k < values.size(); ++k)
+ values[k] = fe.shape_value(i, points[k]);
+ fe.interpolate(local_dofs, values);
+
+ for (unsigned int j=0; j < n_dofs; ++j)
+ N(j,i) = local_dofs[j];
+ }
+
+ for (unsigned int i = 0; i < 4; ++i)
+ {
+ for (unsigned int j = 0; j < 4; ++j)
+ {
+ if (i == j)
+ {
+ deallog << N(i, j) - 1.0;
+ }
+ else
+ {
+ deallog << N(i, j) - 0.0;
+ }
+ if (j + 1 < 4)
+ deallog << " ";
+ else
+ deallog << std::endl;
+ }
+ }
+}
+
+void test_interpolation()
+{
+ Triangulation<2> tr;
+ GridGenerator::hyper_cube(tr, -1, 1);
+ tr.refine_global(2);
+
+ FE_RannacherTurek<2> fe;
+ const unsigned int n_dofs = fe.dofs_per_cell;
+
+ DoFHandler<2> dofh;
+ dofh.initialize(tr, fe);
+
+ Vector<double> input_vector(dofh.n_dofs());
+ for (unsigned int i = 0; i < input_vector.size(); ++i)
+ {
+ input_vector[i] = double(i);
+ }
+
+ Quadrature<2> quadrature(fe.get_generalized_support_points());
+ FEValues<2> fev(fe, quadrature, update_values | update_JxW_values);
+
+ typedef DoFHandler<2>::cell_iterator cell_it;
+ cell_it cell = dofh.begin_active();
+ for (; cell != dofh.end(); ++cell)
+ {
+ fev.reinit(cell);
+
+ std::vector<double> values(quadrature.size());
+ fev.get_function_values(input_vector, values);
+
+ std::vector<double> interpolated_local_dofs(n_dofs);
+ fe.interpolate(interpolated_local_dofs, values);
+
+ Vector<double> local_dofs(n_dofs);
+ cell->get_dof_values(input_vector, local_dofs);
+
+ for (unsigned int j = 0; j < n_dofs; ++j)
+ {
+ deallog << local_dofs[j] - interpolated_local_dofs[j] << " ";
+ }
+ deallog << std::endl;
+ }
+}
+
+int main()
+{
+ initlog();
+
+ test_known_values();
+ test_n_dofs();
+ test_nodal_matrix();
+ test_interpolation();
+
+ return 0;
+}
--- /dev/null
+
+DEAL::0.00000
+DEAL::0.00000
+DEAL::0.00000
+DEAL::0.00000
+DEAL::0
+DEAL::0.00000 -1.04083e-16 0.00000 5.55112e-17
+DEAL::-1.11022e-16 -2.22045e-16 1.11022e-16 1.66533e-16
+DEAL::0.00000 5.55112e-17 0.00000 -1.04083e-16
+DEAL::1.11022e-16 1.66533e-16 -1.11022e-16 -2.22045e-16
+DEAL::-5.55112e-17 -6.66134e-16 0.00000 8.88178e-16
+DEAL::1.11022e-16 -8.88178e-16 0.00000 1.77636e-15
+DEAL::0.00000 8.88178e-16 4.44089e-16 0.00000
+DEAL::0.00000 0.00000 8.88178e-16 0.00000
+DEAL::4.44089e-16 0.00000 0.00000 1.77636e-15
+DEAL::0.00000 0.00000 0.00000 0.00000
+DEAL::0.00000 0.00000 0.00000 0.00000
+DEAL::0.00000 0.00000 0.00000 0.00000
+DEAL::0.00000 0.00000 0.00000 0.00000
+DEAL::3.55271e-15 3.55271e-15 1.77636e-15 0.00000
+DEAL::0.00000 0.00000 0.00000 0.00000
+DEAL::3.55271e-15 3.55271e-15 0.00000 0.00000
+DEAL::0.00000 0.00000 0.00000 0.00000
+DEAL::0.00000 0.00000 0.00000 0.00000
+DEAL::0.00000 0.00000 0.00000 0.00000
+DEAL::0.00000 0.00000 0.00000 0.00000
--- /dev/null
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 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.
+//
+// ---------------------------------------------------------------------
+
+
+// Interfaces being tested
+#include <deal.II/fe/fe_rannacher_turek.h>
+#include <deal.II/base/polynomials_rannacher_turek.h>
+// Interfaces needed for testing
+#include <deal.II/grid/tria.h>
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/dofs/dof_handler.h>
+#include <deal.II/fe/fe_values.h>
+#include <deal.II/base/quadrature_lib.h>
+
+#include "../tests.h"
+
+
+// Regression test for some values of Rannacher Turek element.
+
+void test_values()
+{
+ Triangulation<2> tria;
+ GridGenerator::hyper_cube(tria, 0.0, 1.0);
+
+ FE_RannacherTurek<2> fe;
+ DoFHandler<2> dofh;
+ dofh.initialize(tria, fe);
+
+ QGauss<2> quadrature(8);
+ FEValues<2> fev(fe, quadrature, update_values | update_gradients | update_JxW_values);
+ fev.reinit(dofh.begin_active());
+
+ for (unsigned int i = 0; i < fe.dofs_per_cell; ++i)
+ {
+ for (unsigned int q = 0; q < quadrature.size(); ++q)
+ {
+ deallog << fev.shape_value(i, q) << " ";
+ for (unsigned int d = 0; d < 2; ++d)
+ {
+ deallog << fev.shape_grad(i, q)[d] << " ";
+ }
+ }
+ deallog << std::endl;
+ }
+}
+
+int main()
+{
+ initlog();
+
+ test_values();
+
+ return 0;
+}
--- /dev/null
+
+DEAL::0.730145 -2.44043 1.44043 0.540529 -2.19500 1.44043 0.270527 -1.78830 1.44043 0.00852669 -1.27515 1.44043 -0.174908 -0.724848 1.44043 -0.255006 -0.211701 1.44043 -0.256138 0.195000 1.44043 -0.230145 0.440435 1.44043 0.837950 -2.44043 1.19500 0.648333 -2.19500 1.19500 0.378331 -1.78830 1.19500 0.116331 -1.27515 1.19500 -0.0671033 -0.724848 1.19500 -0.147201 -0.211701 1.19500 -0.148333 0.195000 1.19500 -0.122340 0.440435 1.19500 0.972385 -2.44043 0.788299 0.782768 -2.19500 0.788299 0.512766 -1.78830 0.788299 0.250766 -1.27515 0.788299 0.0673317 -0.724848 0.788299 -0.0127662 -0.211701 0.788299 -0.0138983 0.195000 0.788299 0.0120947 0.440435 0.788299 1.06334 -2.44043 0.275152 0.873719 -2.19500 0.275152 0.603717 -1.78830 0.275152 0.341717 -1.27515 0.275152 0.158283 -0.724848 0.275152 0.0781848 -0.211701 0.275152 0.0770527 0.195000 0.275152 0.103046 0.440435 0.275152 1.06334 -2.44043 -0.275152 0.873719 -2.19500 -0.275152 0.603717 -1.78830 -0.275152 0.341717 -1.27515 -0.275152 0.158283 -0.724848 -0.275152 0.0781848 -0.211701 -0.275152 0.0770527 0.195000 -0.275152 0.103046 0.440435 -0.275152 0.972385 -2.44043 -0.788299 0.782768 -2.19500 -0.788299 0.512766 -1.78830 -0.788299 0.250766 -1.27515 -0.788299 0.0673317 -0.724848 -0.788299 -0.0127662 -0.211701 -0.788299 -0.0138983 0.195000 -0.788299 0.0120947 0.440435 -0.788299 0.837950 -2.44043 -1.19500 0.648333 -2.19500 -1.19500 0.378331 -1.78830 -1.19500 0.116331 -1.27515 -1.19500 -0.0671033 -0.724848 -1.19500 -0.147201 -0.211701 -1.19500 -0.148333 0.195000 -1.19500 -0.122340 0.440435 -1.19500 0.730145 -2.44043 -1.44043 0.540529 -2.19500 -1.44043 0.270527 -1.78830 -1.44043 0.00852669 -1.27515 -1.44043 -0.174908 -0.724848 -1.44043 -0.255006 -0.211701 -1.44043 -0.256138 0.195000 -1.44043 -0.230145 0.440435 -1.44043
+DEAL::-0.230145 -0.440435 1.44043 -0.256138 -0.195000 1.44043 -0.255006 0.211701 1.44043 -0.174908 0.724848 1.44043 0.00852669 1.27515 1.44043 0.270527 1.78830 1.44043 0.540529 2.19500 1.44043 0.730145 2.44043 1.44043 -0.122340 -0.440435 1.19500 -0.148333 -0.195000 1.19500 -0.147201 0.211701 1.19500 -0.0671033 0.724848 1.19500 0.116331 1.27515 1.19500 0.378331 1.78830 1.19500 0.648333 2.19500 1.19500 0.837950 2.44043 1.19500 0.0120947 -0.440435 0.788299 -0.0138983 -0.195000 0.788299 -0.0127662 0.211701 0.788299 0.0673317 0.724848 0.788299 0.250766 1.27515 0.788299 0.512766 1.78830 0.788299 0.782768 2.19500 0.788299 0.972385 2.44043 0.788299 0.103046 -0.440435 0.275152 0.0770527 -0.195000 0.275152 0.0781848 0.211701 0.275152 0.158283 0.724848 0.275152 0.341717 1.27515 0.275152 0.603717 1.78830 0.275152 0.873719 2.19500 0.275152 1.06334 2.44043 0.275152 0.103046 -0.440435 -0.275152 0.0770527 -0.195000 -0.275152 0.0781848 0.211701 -0.275152 0.158283 0.724848 -0.275152 0.341717 1.27515 -0.275152 0.603717 1.78830 -0.275152 0.873719 2.19500 -0.275152 1.06334 2.44043 -0.275152 0.0120947 -0.440435 -0.788299 -0.0138983 -0.195000 -0.788299 -0.0127662 0.211701 -0.788299 0.0673317 0.724848 -0.788299 0.250766 1.27515 -0.788299 0.512766 1.78830 -0.788299 0.782768 2.19500 -0.788299 0.972385 2.44043 -0.788299 -0.122340 -0.440435 -1.19500 -0.148333 -0.195000 -1.19500 -0.147201 0.211701 -1.19500 -0.0671033 0.724848 -1.19500 0.116331 1.27515 -1.19500 0.378331 1.78830 -1.19500 0.648333 2.19500 -1.19500 0.837950 2.44043 -1.19500 -0.230145 -0.440435 -1.44043 -0.256138 -0.195000 -1.44043 -0.255006 0.211701 -1.44043 -0.174908 0.724848 -1.44043 0.00852669 1.27515 -1.44043 0.270527 1.78830 -1.44043 0.540529 2.19500 -1.44043 0.730145 2.44043 -1.44043
+DEAL::0.730145 1.44043 -2.44043 0.837950 1.19500 -2.44043 0.972385 0.788299 -2.44043 1.06334 0.275152 -2.44043 1.06334 -0.275152 -2.44043 0.972385 -0.788299 -2.44043 0.837950 -1.19500 -2.44043 0.730145 -1.44043 -2.44043 0.540529 1.44043 -2.19500 0.648333 1.19500 -2.19500 0.782768 0.788299 -2.19500 0.873719 0.275152 -2.19500 0.873719 -0.275152 -2.19500 0.782768 -0.788299 -2.19500 0.648333 -1.19500 -2.19500 0.540529 -1.44043 -2.19500 0.270527 1.44043 -1.78830 0.378331 1.19500 -1.78830 0.512766 0.788299 -1.78830 0.603717 0.275152 -1.78830 0.603717 -0.275152 -1.78830 0.512766 -0.788299 -1.78830 0.378331 -1.19500 -1.78830 0.270527 -1.44043 -1.78830 0.00852669 1.44043 -1.27515 0.116331 1.19500 -1.27515 0.250766 0.788299 -1.27515 0.341717 0.275152 -1.27515 0.341717 -0.275152 -1.27515 0.250766 -0.788299 -1.27515 0.116331 -1.19500 -1.27515 0.00852669 -1.44043 -1.27515 -0.174908 1.44043 -0.724848 -0.0671033 1.19500 -0.724848 0.0673317 0.788299 -0.724848 0.158283 0.275152 -0.724848 0.158283 -0.275152 -0.724848 0.0673317 -0.788299 -0.724848 -0.0671033 -1.19500 -0.724848 -0.174908 -1.44043 -0.724848 -0.255006 1.44043 -0.211701 -0.147201 1.19500 -0.211701 -0.0127662 0.788299 -0.211701 0.0781848 0.275152 -0.211701 0.0781848 -0.275152 -0.211701 -0.0127662 -0.788299 -0.211701 -0.147201 -1.19500 -0.211701 -0.255006 -1.44043 -0.211701 -0.256138 1.44043 0.195000 -0.148333 1.19500 0.195000 -0.0138983 0.788299 0.195000 0.0770527 0.275152 0.195000 0.0770527 -0.275152 0.195000 -0.0138983 -0.788299 0.195000 -0.148333 -1.19500 0.195000 -0.256138 -1.44043 0.195000 -0.230145 1.44043 0.440435 -0.122340 1.19500 0.440435 0.0120947 0.788299 0.440435 0.103046 0.275152 0.440435 0.103046 -0.275152 0.440435 0.0120947 -0.788299 0.440435 -0.122340 -1.19500 0.440435 -0.230145 -1.44043 0.440435
+DEAL::-0.230145 1.44043 -0.440435 -0.122340 1.19500 -0.440435 0.0120947 0.788299 -0.440435 0.103046 0.275152 -0.440435 0.103046 -0.275152 -0.440435 0.0120947 -0.788299 -0.440435 -0.122340 -1.19500 -0.440435 -0.230145 -1.44043 -0.440435 -0.256138 1.44043 -0.195000 -0.148333 1.19500 -0.195000 -0.0138983 0.788299 -0.195000 0.0770527 0.275152 -0.195000 0.0770527 -0.275152 -0.195000 -0.0138983 -0.788299 -0.195000 -0.148333 -1.19500 -0.195000 -0.256138 -1.44043 -0.195000 -0.255006 1.44043 0.211701 -0.147201 1.19500 0.211701 -0.0127662 0.788299 0.211701 0.0781848 0.275152 0.211701 0.0781848 -0.275152 0.211701 -0.0127662 -0.788299 0.211701 -0.147201 -1.19500 0.211701 -0.255006 -1.44043 0.211701 -0.174908 1.44043 0.724848 -0.0671033 1.19500 0.724848 0.0673317 0.788299 0.724848 0.158283 0.275152 0.724848 0.158283 -0.275152 0.724848 0.0673317 -0.788299 0.724848 -0.0671033 -1.19500 0.724848 -0.174908 -1.44043 0.724848 0.00852669 1.44043 1.27515 0.116331 1.19500 1.27515 0.250766 0.788299 1.27515 0.341717 0.275152 1.27515 0.341717 -0.275152 1.27515 0.250766 -0.788299 1.27515 0.116331 -1.19500 1.27515 0.00852669 -1.44043 1.27515 0.270527 1.44043 1.78830 0.378331 1.19500 1.78830 0.512766 0.788299 1.78830 0.603717 0.275152 1.78830 0.603717 -0.275152 1.78830 0.512766 -0.788299 1.78830 0.378331 -1.19500 1.78830 0.270527 -1.44043 1.78830 0.540529 1.44043 2.19500 0.648333 1.19500 2.19500 0.782768 0.788299 2.19500 0.873719 0.275152 2.19500 0.873719 -0.275152 2.19500 0.782768 -0.788299 2.19500 0.648333 -1.19500 2.19500 0.540529 -1.44043 2.19500 0.730145 1.44043 2.44043 0.837950 1.19500 2.44043 0.972385 0.788299 2.44043 1.06334 0.275152 2.44043 1.06334 -0.275152 2.44043 0.972385 -0.788299 2.44043 0.837950 -1.19500 2.44043 0.730145 -1.44043 2.44043
projects / dealii.git / commitdiff