From 2fe63bb4187bbeb9dbdc6105a76b015daf9dc645 Mon Sep 17 00:00:00 2001 From: Patrick Esser Date: Tue, 30 Jun 2015 15:58:34 +0200 Subject: [PATCH] Add Rannacher-Turek element. Lowest order Rannacher Turek polynomials and FE in 2D and tests. --- doc/news/changes.h | 6 + .../base/polynomials_rannacher_turek.h | 84 +++++++++ include/deal.II/fe/fe_rannacher_turek.h | 103 +++++++++++ source/base/CMakeLists.txt | 2 + source/base/polynomials_rannacher_turek.cc | 172 ++++++++++++++++++ .../base/polynomials_rannacher_turek.inst.in | 22 +++ source/fe/CMakeLists.txt | 2 + source/fe/fe_poly.cc | 1 + source/fe/fe_poly.inst.in | 1 + source/fe/fe_rannacher_turek.cc | 134 ++++++++++++++ source/fe/fe_rannacher_turek.inst.in | 22 +++ tests/fe/fe_rannacher_turek_01.cc | 151 +++++++++++++++ tests/fe/fe_rannacher_turek_01.output | 26 +++ tests/fe/fe_rannacher_turek_02.cc | 66 +++++++ tests/fe/fe_rannacher_turek_02.output | 5 + 15 files changed, 797 insertions(+) create mode 100644 include/deal.II/base/polynomials_rannacher_turek.h create mode 100644 include/deal.II/fe/fe_rannacher_turek.h create mode 100644 source/base/polynomials_rannacher_turek.cc create mode 100644 source/base/polynomials_rannacher_turek.inst.in create mode 100644 source/fe/fe_rannacher_turek.cc create mode 100644 source/fe/fe_rannacher_turek.inst.in create mode 100644 tests/fe/fe_rannacher_turek_01.cc create mode 100644 tests/fe/fe_rannacher_turek_01.output create mode 100644 tests/fe/fe_rannacher_turek_02.cc create mode 100644 tests/fe/fe_rannacher_turek_02.output diff --git a/doc/news/changes.h b/doc/news/changes.h index b4f44d535b..ebcc17138e 100644 --- a/doc/news/changes.h +++ b/doc/news/changes.h @@ -93,6 +93,12 @@ inconvenience this causes. (Jason Sheldon, Wolfgang Bangerth, 2015/08/13) +
  • New: FE_RannacherTurek describes a discontinuous FiniteElement + with vanishing mean values of jumps across faces. +
    + (Patrick Esser, 2015/08/17) +
    • +
  • New: FE_Q_Bubbles describes a FiniteElement based on FE_Q enriched by bubble functions.
    diff --git a/include/deal.II/base/polynomials_rannacher_turek.h b/include/deal.II/base/polynomials_rannacher_turek.h new file mode 100644 index 0000000000..64302bec8e --- /dev/null +++ b/include/deal.II/base/polynomials_rannacher_turek.h @@ -0,0 +1,84 @@ +// --------------------------------------------------------------------- +// +// 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 +#include +#include + +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 +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 &p) const; + /** Gradient of basis function @p i at @p p. + */ + Tensor<1, dim> compute_grad(const unsigned int i, + const Point &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 &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 &unit_point, + std::vector &values, + std::vector > &grads, + std::vector > &grad_grads) const; +}; + + +DEAL_II_NAMESPACE_CLOSE + +#endif diff --git a/include/deal.II/fe/fe_rannacher_turek.h b/include/deal.II/fe/fe_rannacher_turek.h new file mode 100644 index 0000000000..52dc09eed9 --- /dev/null +++ b/include/deal.II/fe/fe_rannacher_turek.h @@ -0,0 +1,103 @@ +// --------------------------------------------------------------------- +// +// 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 +#include +#include +#include +#include + +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. + * + *

    Interpolation

    + * + *

    Node values

    + * The @ref GlossNodes "node values" are moments on faces. + * + *

    Generalized support points

    + * 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 +class FE_RannacherTurek : public FE_Poly, 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 *clone() const; + + virtual void interpolate( + std::vector &local_dofs, + const std::vector &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 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 get_dpo_vector(); +}; + + +DEAL_II_NAMESPACE_CLOSE + +#endif diff --git a/source/base/CMakeLists.txt b/source/base/CMakeLists.txt index 9102a1e0ec..1f45f6ed84 100644 --- a/source/base/CMakeLists.txt +++ b/source/base/CMakeLists.txt @@ -52,6 +52,7 @@ SET(_src polynomial_space.cc polynomials_p.cc polynomials_piecewise.cc + polynomials_rannacher_turek.cc polynomials_raviart_thomas.cc quadrature.cc quadrature_lib.cc @@ -71,6 +72,7 @@ SET(_src SET(_inst data_out_base.inst.in + polynomials_rannacher_turek.inst.in time_stepping.inst.in ) diff --git a/source/base/polynomials_rannacher_turek.cc b/source/base/polynomials_rannacher_turek.cc new file mode 100644 index 0000000000..916715477d --- /dev/null +++ b/source/base/polynomials_rannacher_turek.cc @@ -0,0 +1,172 @@ +// --------------------------------------------------------------------- +// +// 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 +#include + +DEAL_II_NAMESPACE_OPEN + + +template +PolynomialsRannacherTurek::PolynomialsRannacherTurek() +{ + Assert(dim == 2, ExcNotImplemented()); +} + + + +template +double PolynomialsRannacherTurek::compute_value(const unsigned int i, + const Point &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 +Tensor<1, dim> PolynomialsRannacherTurek::compute_grad( + const unsigned int i, + const Point &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 Tensor<2, dim> +PolynomialsRannacherTurek::compute_grad_grad(const unsigned int i, + const Point & /*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 +void PolynomialsRannacherTurek::compute( + const Point &unit_point, + std::vector &values, + std::vector > &grads, + std::vector > &grad_grads) const +{ + const unsigned int n_pols = dealii::GeometryInfo::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 diff --git a/source/base/polynomials_rannacher_turek.inst.in b/source/base/polynomials_rannacher_turek.inst.in new file mode 100644 index 0000000000..32c95b61bd --- /dev/null +++ b/source/base/polynomials_rannacher_turek.inst.in @@ -0,0 +1,22 @@ +// --------------------------------------------------------------------- +// +// 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; + } + diff --git a/source/fe/CMakeLists.txt b/source/fe/CMakeLists.txt index 73fee37d1e..228cd4e686 100644 --- a/source/fe/CMakeLists.txt +++ b/source/fe/CMakeLists.txt @@ -39,6 +39,7 @@ SET(_src 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 @@ -78,6 +79,7 @@ SET(_inst 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 diff --git a/source/fe/fe_poly.cc b/source/fe/fe_poly.cc index ebd25e7906..9fe3a4650d 100644 --- a/source/fe/fe_poly.cc +++ b/source/fe/fe_poly.cc @@ -20,6 +20,7 @@ #include #include #include +#include #include #include #include diff --git a/source/fe/fe_poly.inst.in b/source/fe/fe_poly.inst.in index dcd33ed098..d9dd85373a 100644 --- a/source/fe/fe_poly.inst.in +++ b/source/fe/fe_poly.inst.in @@ -24,6 +24,7 @@ for (deal_II_dimension : DIMENSIONS; deal_II_space_dimension : SPACE_DIMENSIONS template class FE_Poly >, deal_II_dimension, deal_II_space_dimension>; template class FE_Poly, deal_II_dimension, deal_II_space_dimension>; template class FE_Poly, deal_II_dimension, deal_II_space_dimension>; + template class FE_Poly, deal_II_dimension, deal_II_space_dimension>; #endif } diff --git a/source/fe/fe_rannacher_turek.cc b/source/fe/fe_rannacher_turek.cc new file mode 100644 index 0000000000..4f901e52d0 --- /dev/null +++ b/source/fe/fe_rannacher_turek.cc @@ -0,0 +1,134 @@ +// --------------------------------------------------------------------- +// +// 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 +#include +#include + +#include + + +DEAL_II_NAMESPACE_OPEN + + +template +FE_RannacherTurek::FE_RannacherTurek(const unsigned int degree, + const unsigned int n_face_support_points) : + FE_Poly, dim>( + PolynomialsRannacherTurek(), + FiniteElementData(this->get_dpo_vector(), + 1, + 2, + FiniteElementData::L2), + std::vector(4, false), // restriction not implemented + std::vector(4, std::vector(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 +std::vector FE_RannacherTurek::get_dpo_vector() +{ + std::vector dpo(dim + 1, 0); + dpo[dim - 1] = 1; + + return dpo; +} + + + +template +std::string FE_RannacherTurek::get_name() const +{ + std::ostringstream namebuf; + namebuf << "FE_RannacherTurek" + << "<" << dim << ">" + << "(" << this->degree << ", " << this-n_face_support_points << ")"; + return namebuf.str(); +} + + + +template +FiniteElement *FE_RannacherTurek::clone() const +{ + return new FE_RannacherTurek(this->degree, this->n_face_support_points); +} + + + +template +void FE_RannacherTurek::initialize_support_points() +{ + Assert(dim == 2, ExcNotImplemented()); + dealii::QGauss 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(0, 1 - face_quadrature.point(q)(0)); + this->generalized_support_points[1*face_quadrature.size() + q] = + dealii::Point(1, 1 - face_quadrature.point(q)(0)); + this->generalized_support_points[2*face_quadrature.size() + q] = + dealii::Point(face_quadrature.point(q)(0), 0); + this->generalized_support_points[3*face_quadrature.size() + q] = + dealii::Point(face_quadrature.point(q)(0), 1); + } +} + + + +template +void FE_RannacherTurek::interpolate( + std::vector &local_dofs, + const std::vector &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::const_iterator value = values.begin(); + for (unsigned int face = 0; + face < dealii::GeometryInfo::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 diff --git a/source/fe/fe_rannacher_turek.inst.in b/source/fe/fe_rannacher_turek.inst.in new file mode 100644 index 0000000000..5c165e24bd --- /dev/null +++ b/source/fe/fe_rannacher_turek.inst.in @@ -0,0 +1,22 @@ +// --------------------------------------------------------------------- +// +// 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; + } + diff --git a/tests/fe/fe_rannacher_turek_01.cc b/tests/fe/fe_rannacher_turek_01.cc new file mode 100644 index 0000000000..55b0d6659d --- /dev/null +++ b/tests/fe/fe_rannacher_turek_01.cc @@ -0,0 +1,151 @@ +// --------------------------------------------------------------------- +// +// 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 +#include +// Interfaces needed for testing +#include +#include +#include +#include +#include + +#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 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 > &points = fe.get_generalized_support_points(); + std::vector values(points.size()); + std::vector 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 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 values(quadrature.size()); + fev.get_function_values(input_vector, values); + + std::vector interpolated_local_dofs(n_dofs); + fe.interpolate(interpolated_local_dofs, values); + + Vector 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; +} diff --git a/tests/fe/fe_rannacher_turek_01.output b/tests/fe/fe_rannacher_turek_01.output new file mode 100644 index 0000000000..46c8ddb079 --- /dev/null +++ b/tests/fe/fe_rannacher_turek_01.output @@ -0,0 +1,26 @@ + +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 diff --git a/tests/fe/fe_rannacher_turek_02.cc b/tests/fe/fe_rannacher_turek_02.cc new file mode 100644 index 0000000000..22a26f292e --- /dev/null +++ b/tests/fe/fe_rannacher_turek_02.cc @@ -0,0 +1,66 @@ +// --------------------------------------------------------------------- +// +// 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 +#include +// Interfaces needed for testing +#include +#include +#include +#include +#include + +#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; +} diff --git a/tests/fe/fe_rannacher_turek_02.output b/tests/fe/fe_rannacher_turek_02.output new file mode 100644 index 0000000000..5eebd5b644 --- /dev/null +++ b/tests/fe/fe_rannacher_turek_02.output @@ -0,0 +1,5 @@ + +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 -- 2.39.5