--- /dev/null
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2023 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.md at
+// the top level directory of deal.II.
+//
+// ---------------------------------------------------------------------
+
+
+
+// this function tests the correctness of the implementation of matrix-free
+// operations in getting the function values, the function gradients, and the
+// function Laplacians on a hyperball mesh with various orientations for a
+// quadratic function. The test case is without any constraints
+
+#include <deal.II/base/function.h>
+#include <deal.II/base/logstream.h>
+#include <deal.II/base/utilities.h>
+
+#include <deal.II/dofs/dof_handler.h>
+#include <deal.II/dofs/dof_tools.h>
+
+#include <deal.II/fe/fe_raviart_thomas.h>
+#include <deal.II/fe/mapping_q.h>
+
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/tria.h>
+
+#include <deal.II/lac/affine_constraints.h>
+#include <deal.II/lac/vector.h>
+
+#include <deal.II/matrix_free/fe_evaluation.h>
+#include <deal.II/matrix_free/matrix_free.h>
+
+#include <deal.II/numerics/vector_tools.h>
+
+#include <fstream>
+#include <iostream>
+
+#include "../tests.h"
+
+
+template <int dim>
+class CompareFunction : public Function<dim>
+{
+public:
+ CompareFunction()
+ : Function<dim>(dim)
+ {}
+
+ virtual double
+ value(const Point<dim> &p, const unsigned int component) const
+ {
+ double value = (1.2 - 0.5 * component) * p[0] * p[0] + 0.4 + component;
+ for (unsigned int d = 1; d < dim; ++d)
+ value -= (2.7 - 0.6 * component) * d * p[d] * p[d];
+ return value;
+ }
+
+ virtual Tensor<1, dim>
+ gradient(const Point<dim> &p, const unsigned int component) const
+ {
+ Tensor<1, dim> grad;
+ grad[0] = (1.2 - 0.5 * component) * p[0] * 2;
+ for (unsigned int d = 1; d < dim; ++d)
+ grad[d] = -(2.7 - 0.6 * component) * d * p[d] * 2;
+ return grad;
+ }
+};
+
+
+
+template <int dim,
+ int fe_degree,
+ int n_q_points_1d = fe_degree + 1,
+ typename Number = double>
+class MatrixFreeTest
+{
+public:
+ MatrixFreeTest(const MatrixFree<dim, Number> &data_in)
+ : data(data_in){};
+
+ MatrixFreeTest(const MatrixFree<dim, Number> &data_in,
+ const Mapping<dim> &mapping)
+ : data(data_in){};
+
+ virtual ~MatrixFreeTest()
+ {}
+
+ // make function virtual to allow derived classes to define a different
+ // function
+ virtual void
+ cell(const MatrixFree<dim, Number> &data,
+ Vector<Number> &,
+ const Vector<Number> &src,
+ const std::pair<unsigned int, unsigned int> &cell_range) const
+ {
+ FEEvaluation<dim, fe_degree, n_q_points_1d, dim, Number> fe_eval(data);
+
+ CompareFunction<dim> function;
+
+ for (unsigned int cell = cell_range.first; cell < cell_range.second; ++cell)
+ {
+ fe_eval.reinit(cell);
+ fe_eval.read_dof_values(src);
+ fe_eval.evaluate(EvaluationFlags::values | EvaluationFlags::gradients);
+
+ for (unsigned int j = 0; j < data.n_active_entries_per_cell_batch(cell);
+ ++j)
+ for (unsigned int q = 0; q < fe_eval.n_q_points; ++q)
+ {
+ Point<dim> p;
+ for (unsigned int d = 0; d < dim; ++d)
+ p[d] = fe_eval.quadrature_point(q)[d][j];
+ for (unsigned int d = 0; d < dim; ++d)
+ {
+ cell_errors[0][d] += std::abs(fe_eval.get_value(q)[d][j] -
+ function.value(p, d)) *
+ fe_eval.JxW(q)[j];
+ for (unsigned int e = 0; e < dim; ++e)
+ cell_errors[1][d] +=
+ std::abs(fe_eval.get_gradient(q)[d][e][j] -
+ function.gradient(p, d)[e]) *
+ fe_eval.JxW(q)[j];
+ }
+ double divergence = 0;
+ for (unsigned int d = 0; d < dim; ++d)
+ divergence += function.gradient(p, d)[d];
+ cell_errors[2][0] +=
+ std::abs(fe_eval.get_divergence(q)[j] - divergence) *
+ fe_eval.JxW(q)[j];
+ }
+ }
+ }
+
+ virtual void
+ face(const MatrixFree<dim, Number> &data,
+ Vector<Number> &,
+ const Vector<Number> &src,
+ const std::pair<unsigned int, unsigned int> &face_range) const
+ {
+ FEFaceEvaluation<dim, fe_degree, n_q_points_1d, dim, Number> fe_evalm(data,
+ true);
+ FEFaceEvaluation<dim, fe_degree, n_q_points_1d, dim, Number> fe_evalp(
+ data, false);
+
+ CompareFunction<dim> function;
+
+ for (unsigned int face = face_range.first; face < face_range.second; ++face)
+ {
+ fe_evalm.reinit(face);
+ fe_evalm.read_dof_values(src);
+ fe_evalm.evaluate(EvaluationFlags::values | EvaluationFlags::gradients |
+ EvaluationFlags::hessians);
+ fe_evalp.reinit(face);
+ fe_evalp.read_dof_values(src);
+ fe_evalp.evaluate(EvaluationFlags::values | EvaluationFlags::gradients |
+ EvaluationFlags::hessians);
+
+ for (unsigned int j = 0; j < VectorizedArray<Number>::size(); ++j)
+ {
+ // skip empty components in VectorizedArray
+ if (data.get_face_info(face).cells_interior[j] ==
+ numbers::invalid_unsigned_int)
+ break;
+ for (unsigned int q = 0; q < fe_evalm.n_q_points; ++q)
+ {
+ Point<dim> p;
+
+ // interior face
+ for (unsigned int d = 0; d < dim; ++d)
+ p[d] = fe_evalm.quadrature_point(q)[d][j];
+ for (unsigned int d = 0; d < dim; ++d)
+ {
+ facem_errors[0][d] += std::abs(fe_evalm.get_value(q)[d][j] -
+ function.value(p, d)) *
+ fe_evalm.JxW(q)[j];
+ for (unsigned int e = 0; e < dim; ++e)
+ {
+ facem_errors[1][d] +=
+ std::abs(fe_evalm.get_gradient(q)[d][e][j] -
+ function.gradient(p, d)[e]) *
+ fe_evalm.JxW(q)[j];
+ }
+ }
+ double divergence = 0;
+ for (unsigned int d = 0; d < dim; ++d)
+ divergence += function.gradient(p, d)[d];
+ facem_errors[2][0] +=
+ std::abs(fe_evalm.get_divergence(q)[j] - divergence) *
+ fe_evalm.JxW(q)[j];
+
+ // exterior face
+ for (unsigned int d = 0; d < dim; ++d)
+ {
+ facep_errors[0][d] += std::abs(fe_evalp.get_value(q)[d][j] -
+ function.value(p, d)) *
+ fe_evalm.JxW(q)[j];
+ for (unsigned int e = 0; e < dim; ++e)
+ facep_errors[1][d] +=
+ std::abs(fe_evalp.get_gradient(q)[d][e][j] -
+ function.gradient(p, d)[e]) *
+ fe_evalm.JxW(q)[j];
+ }
+ facep_errors[2][0] +=
+ std::abs(fe_evalp.get_divergence(q)[j] - divergence) *
+ fe_evalm.JxW(q)[j];
+ }
+ }
+ }
+ }
+
+ virtual void
+ boundary(const MatrixFree<dim, Number> &data,
+ Vector<Number> &,
+ const Vector<Number> &src,
+ const std::pair<unsigned int, unsigned int> &face_range) const
+ {
+ FEFaceEvaluation<dim, fe_degree, n_q_points_1d, dim, Number> fe_evalm(data,
+ true);
+
+ CompareFunction<dim> function;
+
+ for (unsigned int face = face_range.first; face < face_range.second; ++face)
+ {
+ fe_evalm.reinit(face);
+ fe_evalm.read_dof_values(src);
+ fe_evalm.evaluate(EvaluationFlags::values | EvaluationFlags::gradients |
+ EvaluationFlags::hessians);
+
+ for (unsigned int j = 0; j < VectorizedArray<Number>::size(); ++j)
+ {
+ // skip empty components in VectorizedArray
+ if (data.get_face_info(face).cells_interior[j] ==
+ numbers::invalid_unsigned_int)
+ break;
+ for (unsigned int q = 0; q < fe_evalm.n_q_points; ++q)
+ {
+ Point<dim> p;
+ for (unsigned int d = 0; d < dim; ++d)
+ p[d] = fe_evalm.quadrature_point(q)[d][j];
+ for (unsigned int d = 0; d < dim; ++d)
+ {
+ boundary_errors[0][d] +=
+ std::abs(fe_evalm.get_value(q)[d][j] -
+ function.value(p, d)) *
+ fe_evalm.JxW(q)[j];
+ for (unsigned int e = 0; e < dim; ++e)
+ boundary_errors[1][d] +=
+ std::abs(fe_evalm.get_gradient(q)[d][e][j] -
+ function.gradient(p, d)[e]) *
+ fe_evalm.JxW(q)[j];
+ }
+ double divergence = 0;
+ for (unsigned int d = 0; d < dim; ++d)
+ divergence += function.gradient(p, d)[d];
+ boundary_errors[2][0] +=
+ std::abs(fe_evalm.get_divergence(q)[j] - divergence) *
+ fe_evalm.JxW(q)[j];
+ }
+ }
+ }
+ }
+
+
+
+ static void
+ print_error(const std::string &text,
+ const dealii::ndarray<double, 3, dim> &array)
+ {
+ deallog << "Error " << std::left << std::setw(6) << text << " values: ";
+ for (unsigned int d = 0; d < dim; ++d)
+ deallog << array[0][d] << " ";
+ deallog << std::endl;
+ deallog << "Error " << std::left << std::setw(6) << text << " gradients: ";
+ for (unsigned int d = 0; d < dim; ++d)
+ deallog << array[1][d] << " ";
+ deallog << std::endl;
+ deallog << "Error " << std::left << std::setw(6) << text << " divergence: ";
+ deallog << array[2][0] << " ";
+ deallog << std::endl;
+ }
+
+ void
+ test_functions(const Vector<Number> &src) const
+ {
+ for (unsigned int d = 0; d < dim; ++d)
+ for (unsigned int i = 0; i < 3; ++i)
+ {
+ cell_errors[i][d] = 0;
+ facem_errors[i][d] = 0;
+ facep_errors[i][d] = 0;
+ boundary_errors[i][d] = 0;
+ }
+
+ Vector<Number> dst_dummy;
+ data.loop(&MatrixFreeTest::cell,
+ &MatrixFreeTest::face,
+ &MatrixFreeTest::boundary,
+ this,
+ dst_dummy,
+ src);
+
+ print_error("cell", cell_errors);
+ print_error("face-", facem_errors);
+ print_error("face+", facep_errors);
+ print_error("face b", boundary_errors);
+ deallog << std::endl;
+ };
+
+protected:
+ const MatrixFree<dim, Number> &data;
+ mutable dealii::ndarray<double, 3, dim> cell_errors, facem_errors,
+ facep_errors, boundary_errors;
+};
+
+
+
+template <int dim, int fe_degree, typename number>
+void
+do_test(const DoFHandler<dim> &dof,
+ const AffineConstraints<double> &constraints)
+{
+ deallog << "Testing " << dof.get_fe().get_name() << std::endl;
+ // use this for info on problem
+ // std::cout << "Number of cells: " <<
+ // dof.get_triangulation().n_active_cells()
+ // << std::endl;
+ // std::cout << "Number of degrees of freedom: " << dof.n_dofs() << std::endl;
+ // std::cout << "Number of constraints: " << constraints.n_constraints() <<
+ // std::endl;
+
+ MappingQ<dim> mapping(dof.get_fe().degree);
+ Vector<number> interpolated(dof.n_dofs());
+ VectorTools::interpolate(mapping, dof, CompareFunction<dim>(), interpolated);
+
+ constraints.distribute(interpolated);
+ MatrixFree<dim, number> mf_data;
+ {
+ const QGauss<1> quad(dof.get_fe().degree + 1);
+ typename MatrixFree<dim, number>::AdditionalData data;
+ data.tasks_parallel_scheme = MatrixFree<dim, number>::AdditionalData::none;
+ data.mapping_update_flags = update_gradients | update_quadrature_points;
+ data.mapping_update_flags_boundary_faces =
+ update_gradients | update_quadrature_points;
+ data.mapping_update_flags_inner_faces =
+ update_gradients | update_quadrature_points;
+ mf_data.reinit(mapping, dof, constraints, quad, data);
+ }
+
+ MatrixFreeTest<dim, fe_degree, fe_degree + 1, number> mf(mf_data);
+ mf.test_functions(interpolated);
+}
+
+
+
+template <int dim, int fe_degree>
+void
+test()
+{
+ Triangulation<dim> tria;
+ GridGenerator::hyper_ball(tria, Point<dim>(), 1.);
+ tria.refine_global(1);
+
+ {
+ FE_RaviartThomasNodal<dim> fe(fe_degree - 1);
+ DoFHandler<dim> dof(tria);
+ dof.distribute_dofs(fe);
+
+ AffineConstraints<double> constraints;
+ constraints.close();
+ deallog.push("L1");
+ if (fe_degree > 2)
+ do_test<dim, -1, double>(dof, constraints);
+ else
+ do_test<dim, fe_degree, double>(dof, constraints);
+ deallog.pop();
+
+ tria.refine_global(1);
+ dof.distribute_dofs(fe);
+ deallog.push("L2");
+ if (fe_degree > 2)
+ do_test<dim, -1, double>(dof, constraints);
+ else
+ do_test<dim, fe_degree, double>(dof, constraints);
+ deallog.pop();
+ }
+}
+
+
+
+int
+main()
+{
+ initlog();
+
+ deallog << std::setprecision(5);
+ {
+ deallog.push("2d");
+ test<2, 1>();
+ test<2, 2>();
+ test<2, 3>();
+ test<2, 4>();
+ deallog.pop();
+ deallog.push("3d");
+ test<3, 1>();
+ test<3, 2>();
+ test<3, 3>();
+ deallog.pop();
+ }
+}
--- /dev/null
+
+DEAL:2d:L1::Testing FE_RaviartThomasNodal<2>(0)
+DEAL:2d:L1::Error cell values: 0.76600 0.72535
+DEAL:2d:L1::Error cell gradients: 8.4251 6.3721
+DEAL:2d:L1::Error cell divergence: 4.0337
+DEAL:2d:L1::Error face- values: 4.2318 3.8392
+DEAL:2d:L1::Error face- gradients: 39.111 37.373
+DEAL:2d:L1::Error face- divergence: 26.921
+DEAL:2d:L1::Error face+ values: 3.9437 3.6201
+DEAL:2d:L1::Error face+ gradients: 40.083 33.783
+DEAL:2d:L1::Error face+ divergence: 20.281
+DEAL:2d:L1::Error face b values: 3.2781 2.1558
+DEAL:2d:L1::Error face b gradients: 24.408 13.913
+DEAL:2d:L1::Error face b divergence: 7.4894
+DEAL:2d:L1::
+DEAL:2d:L2::Testing FE_RaviartThomasNodal<2>(0)
+DEAL:2d:L2::Error cell values: 0.48352 0.39872
+DEAL:2d:L2::Error cell gradients: 9.2757 6.6556
+DEAL:2d:L2::Error cell divergence: 4.3348
+DEAL:2d:L2::Error face- values: 5.6172 4.5792
+DEAL:2d:L2::Error face- gradients: 90.179 77.171
+DEAL:2d:L2::Error face- divergence: 59.588
+DEAL:2d:L2::Error face+ values: 5.3538 4.5029
+DEAL:2d:L2::Error face+ gradients: 86.410 65.332
+DEAL:2d:L2::Error face+ divergence: 45.670
+DEAL:2d:L2::Error face b values: 1.8273 1.0202
+DEAL:2d:L2::Error face b gradients: 23.810 14.039
+DEAL:2d:L2::Error face b divergence: 5.7176
+DEAL:2d:L2::
+DEAL:2d:L1::Testing FE_RaviartThomasNodal<2>(1)
+DEAL:2d:L1::Error cell values: 0.35581 0.39956
+DEAL:2d:L1::Error cell gradients: 5.1255 5.8943
+DEAL:2d:L1::Error cell divergence: 5.9794
+DEAL:2d:L1::Error face- values: 1.7388 2.2056
+DEAL:2d:L1::Error face- gradients: 38.435 44.170
+DEAL:2d:L1::Error face- divergence: 37.888
+DEAL:2d:L1::Error face+ values: 1.5105 1.9910
+DEAL:2d:L1::Error face+ gradients: 29.229 32.776
+DEAL:2d:L1::Error face+ divergence: 32.188
+DEAL:2d:L1::Error face b values: 1.1896 1.3149
+DEAL:2d:L1::Error face b gradients: 11.750 11.262
+DEAL:2d:L1::Error face b divergence: 10.617
+DEAL:2d:L1::
+DEAL:2d:L2::Testing FE_RaviartThomasNodal<2>(1)
+DEAL:2d:L2::Error cell values: 0.14354 0.14722
+DEAL:2d:L2::Error cell gradients: 4.1713 4.8369
+DEAL:2d:L2::Error cell divergence: 5.0393
+DEAL:2d:L2::Error face- values: 1.8280 2.2410
+DEAL:2d:L2::Error face- gradients: 69.298 82.221
+DEAL:2d:L2::Error face- divergence: 79.684
+DEAL:2d:L2::Error face+ values: 1.5687 2.0843
+DEAL:2d:L2::Error face+ gradients: 53.012 62.748
+DEAL:2d:L2::Error face+ divergence: 66.862
+DEAL:2d:L2::Error face b values: 0.45449 0.44056
+DEAL:2d:L2::Error face b gradients: 7.7589 7.2442
+DEAL:2d:L2::Error face b divergence: 6.1239
+DEAL:2d:L2::
+DEAL:2d:L1::Testing FE_RaviartThomasNodal<2>(2)
+DEAL:2d:L1::Error cell values: 0.13980 0.17077
+DEAL:2d:L1::Error cell gradients: 3.7272 4.8648
+DEAL:2d:L1::Error cell divergence: 4.9444
+DEAL:2d:L1::Error face- values: 1.3674 1.8556
+DEAL:2d:L1::Error face- gradients: 43.476 58.212
+DEAL:2d:L1::Error face- divergence: 56.234
+DEAL:2d:L1::Error face+ values: 1.0984 1.6891
+DEAL:2d:L1::Error face+ gradients: 29.783 42.660
+DEAL:2d:L1::Error face+ divergence: 46.665
+DEAL:2d:L1::Error face b values: 0.41366 0.37645
+DEAL:2d:L1::Error face b gradients: 5.5217 5.4703
+DEAL:2d:L1::Error face b divergence: 4.2204
+DEAL:2d:L1::
+DEAL:2d:L2::Testing FE_RaviartThomasNodal<2>(2)
+DEAL:2d:L2::Error cell values: 0.060321 0.077774
+DEAL:2d:L2::Error cell gradients: 3.5424 4.6692
+DEAL:2d:L2::Error cell divergence: 5.0762
+DEAL:2d:L2::Error face- values: 1.4779 1.9132
+DEAL:2d:L2::Error face- gradients: 85.256 112.58
+DEAL:2d:L2::Error face- divergence: 116.99
+DEAL:2d:L2::Error face+ values: 1.1908 1.7800
+DEAL:2d:L2::Error face+ gradients: 61.373 87.594
+DEAL:2d:L2::Error face+ divergence: 99.172
+DEAL:2d:L2::Error face b values: 0.13182 0.13272
+DEAL:2d:L2::Error face b gradients: 4.2877 4.3459
+DEAL:2d:L2::Error face b divergence: 3.9350
+DEAL:2d:L2::
+DEAL:2d:L1::Testing FE_RaviartThomasNodal<2>(3)
+DEAL:2d:L1::Error cell values: 0.083187 0.10755
+DEAL:2d:L1::Error cell gradients: 3.5511 4.7393
+DEAL:2d:L1::Error cell divergence: 5.1233
+DEAL:2d:L1::Error face- values: 1.3081 1.7200
+DEAL:2d:L1::Error face- gradients: 60.495 78.271
+DEAL:2d:L1::Error face- divergence: 78.129
+DEAL:2d:L1::Error face+ values: 1.0234 1.5766
+DEAL:2d:L1::Error face+ gradients: 40.871 60.436
+DEAL:2d:L1::Error face+ divergence: 68.428
+DEAL:2d:L1::Error face b values: 0.17779 0.18097
+DEAL:2d:L1::Error face b gradients: 4.1181 4.1715
+DEAL:2d:L1::Error face b divergence: 4.0317
+DEAL:2d:L1::
+DEAL:2d:L2::Testing FE_RaviartThomasNodal<2>(3)
+DEAL:2d:L2::Error cell values: 0.041058 0.052901
+DEAL:2d:L2::Error cell gradients: 3.6350 4.7911
+DEAL:2d:L2::Error cell divergence: 5.2997
+DEAL:2d:L2::Error face- values: 1.3816 1.7638
+DEAL:2d:L2::Error face- gradients: 120.15 153.92
+DEAL:2d:L2::Error face- divergence: 162.33
+DEAL:2d:L2::Error face+ values: 1.0875 1.6414
+DEAL:2d:L2::Error face+ gradients: 85.185 124.79
+DEAL:2d:L2::Error face+ divergence: 143.62
+DEAL:2d:L2::Error face b values: 0.081640 0.081532
+DEAL:2d:L2::Error face b gradients: 4.1275 4.1225
+DEAL:2d:L2::Error face b divergence: 4.0589
+DEAL:2d:L2::
+DEAL:3d:L1::Testing FE_RaviartThomasNodal<3>(0)
+DEAL:3d:L1::Error cell values: 1.8429 1.3769 1.2562
+DEAL:3d:L1::Error cell gradients: 25.242 18.035 15.467
+DEAL:3d:L1::Error cell divergence: 8.4549
+DEAL:3d:L1::Error face- values: 12.971 9.8571 10.337
+DEAL:3d:L1::Error face- gradients: 157.73 126.65 135.62
+DEAL:3d:L1::Error face- divergence: 65.605
+DEAL:3d:L1::Error face+ values: 12.925 10.240 8.7290
+DEAL:3d:L1::Error face+ gradients: 174.07 131.18 131.32
+DEAL:3d:L1::Error face+ divergence: 71.384
+DEAL:3d:L1::Error face b values: 11.921 7.4509 4.5886
+DEAL:3d:L1::Error face b gradients: 99.045 69.112 41.259
+DEAL:3d:L1::Error face b divergence: 26.234
+DEAL:3d:L1::
+DEAL:3d:L2::Testing FE_RaviartThomasNodal<3>(0)
+DEAL:3d:L2::Error cell values: 1.3891 1.0210 0.95375
+DEAL:3d:L2::Error cell gradients: 33.030 22.592 19.619
+DEAL:3d:L2::Error cell divergence: 10.132
+DEAL:3d:L2::Error face- values: 19.343 14.320 14.446
+DEAL:3d:L2::Error face- gradients: 392.29 286.46 283.01
+DEAL:3d:L2::Error face- divergence: 156.90
+DEAL:3d:L2::Error face+ values: 19.734 15.160 13.949
+DEAL:3d:L2::Error face+ gradients: 418.42 302.38 297.37
+DEAL:3d:L2::Error face+ divergence: 168.21
+DEAL:3d:L2::Error face b values: 8.2201 5.3245 3.6886
+DEAL:3d:L2::Error face b gradients: 119.61 81.596 53.200
+DEAL:3d:L2::Error face b divergence: 24.468
+DEAL:3d:L2::
+DEAL:3d:L1::Testing FE_RaviartThomasNodal<3>(1)
+DEAL:3d:L1::Error cell values: 1.1615 1.0843 1.2103
+DEAL:3d:L1::Error cell gradients: 18.490 15.134 15.206
+DEAL:3d:L1::Error cell divergence: 14.588
+DEAL:3d:L1::Error face- values: 6.8276 4.7251 6.8680
+DEAL:3d:L1::Error face- gradients: 141.86 108.58 131.14
+DEAL:3d:L1::Error face- divergence: 101.48
+DEAL:3d:L1::Error face+ values: 5.9713 6.0931 6.7026
+DEAL:3d:L1::Error face+ gradients: 131.50 119.62 118.85
+DEAL:3d:L1::Error face+ divergence: 112.83
+DEAL:3d:L1::Error face b values: 3.8486 4.4996 4.0159
+DEAL:3d:L1::Error face b gradients: 70.612 56.268 48.614
+DEAL:3d:L1::Error face b divergence: 39.209
+DEAL:3d:L1::
+DEAL:3d:L2::Testing FE_RaviartThomasNodal<3>(1)
+DEAL:3d:L2::Error cell values: 0.46499 0.38144 0.43855
+DEAL:3d:L2::Error cell gradients: 13.575 11.045 12.602
+DEAL:3d:L2::Error cell divergence: 12.129
+DEAL:3d:L2::Error face- values: 6.5588 4.4357 6.5926
+DEAL:3d:L2::Error face- gradients: 238.60 175.06 237.70
+DEAL:3d:L2::Error face- divergence: 214.00
+DEAL:3d:L2::Error face+ values: 5.7699 5.6976 6.2465
+DEAL:3d:L2::Error face+ gradients: 215.48 204.34 213.10
+DEAL:3d:L2::Error face+ divergence: 226.34
+DEAL:3d:L2::Error face b values: 1.9464 1.6908 1.5795
+DEAL:3d:L2::Error face b gradients: 49.010 39.276 37.868
+DEAL:3d:L2::Error face b divergence: 28.000
+DEAL:3d:L2::
+DEAL:3d:L1::Testing FE_RaviartThomasNodal<3>(2)
+DEAL:3d:L1::Error cell values: 0.37828 0.32881 0.38922
+DEAL:3d:L1::Error cell gradients: 10.134 8.9301 11.299
+DEAL:3d:L1::Error cell divergence: 11.491
+DEAL:3d:L1::Error face- values: 3.8008 2.5231 4.4875
+DEAL:3d:L1::Error face- gradients: 122.69 87.225 147.32
+DEAL:3d:L1::Error face- divergence: 132.72
+DEAL:3d:L1::Error face+ values: 3.1532 3.5726 3.9086
+DEAL:3d:L1::Error face+ gradients: 94.017 115.09 119.21
+DEAL:3d:L1::Error face+ divergence: 145.70
+DEAL:3d:L1::Error face b values: 1.5283 1.3653 1.4527
+DEAL:3d:L1::Error face b gradients: 28.290 24.217 27.985
+DEAL:3d:L1::Error face b divergence: 22.873
+DEAL:3d:L1::
+DEAL:3d:L2::Testing FE_RaviartThomasNodal<3>(2)
+DEAL:3d:L2::Error cell values: 0.15947 0.13646 0.18046
+DEAL:3d:L2::Error cell gradients: 9.1649 7.9294 10.660
+DEAL:3d:L2::Error cell divergence: 12.366
+DEAL:3d:L2::Error face- values: 4.0172 2.6015 4.7501
+DEAL:3d:L2::Error face- gradients: 237.82 163.03 286.37
+DEAL:3d:L2::Error face- divergence: 299.49
+DEAL:3d:L2::Error face+ values: 3.2666 3.7201 4.0280
+DEAL:3d:L2::Error face+ gradients: 188.38 218.02 236.01
+DEAL:3d:L2::Error face+ divergence: 311.63
+DEAL:3d:L2::Error face b values: 0.58416 0.51535 0.64034
+DEAL:3d:L2::Error face b gradients: 22.761 20.071 25.067
+DEAL:3d:L2::Error face b divergence: 25.294
+DEAL:3d:L2::
projects / dealii.git / commitdiff