From 7acc9a3af566a1ae0743632b567265baf320cbd5 Mon Sep 17 00:00:00 2001 From: Graham Harper Date: Tue, 3 Jul 2018 21:23:34 +0000 Subject: [PATCH] Add tests for the BR element. --- tests/fe/br_approximation_01.cc | 518 +++++++++ tests/fe/br_approximation_01.output | 1516 +++++++++++++++++++++++++++ tests/fe/fe_br.cc | 141 +++ tests/fe/fe_br.output | 131 +++ 4 files changed, 2306 insertions(+) create mode 100644 tests/fe/br_approximation_01.cc create mode 100644 tests/fe/br_approximation_01.output create mode 100644 tests/fe/fe_br.cc create mode 100644 tests/fe/fe_br.output diff --git a/tests/fe/br_approximation_01.cc b/tests/fe/br_approximation_01.cc new file mode 100644 index 0000000000..e8457e30bb --- /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 +#include + +#include + +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include + +#include +#include + +#include +#include +#include +#include +#include +#include +#include + +#include +#include +#include + + + +template +class TestMap1 : public Function +{ +public: + TestMap1(const unsigned int n_components) + : Function(n_components) + {} + + virtual ~TestMap1() + {} + + virtual double + value(const Point &p, const unsigned int component = 0) const; + + void + vector_value(const Point &p, Vector &return_value) const; +}; + + + +template +double +TestMap1::value(const Point &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 +void +TestMap1::vector_value(const Point &p, + Vector & 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 +class TestDef1 : public Function +{ +private: + const double phi; + +public: + TestDef1(const unsigned int n_components, const double ph) + : Function(n_components) + , phi(ph) + {} + + virtual ~TestDef1() + {} + + virtual double + value(const Point &p, const unsigned int component = 0) const; + + void + vector_value(const Point &p, Vector &return_value) const; +}; + + + +template +double +TestDef1::value(const Point &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 +void +TestDef1::vector_value(const Point &p, + Vector & 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 +class TestDef2 : public Function +{ +private: + const double scale; + +public: + TestDef2(const unsigned int n_components, const double sc) + : Function(n_components) + , scale(sc) + {} + + virtual ~TestDef2() + {} + + virtual double + value(const Point &p, const unsigned int component = 0) const; + + void + vector_value(const Point &p, Vector &return_value) const; +}; + + +template +double +TestDef2::value(const Point &p, const unsigned int component) const +{ + double x = p(0), y = p(1); + + if (component == 0) + return scale * x; + else + return scale * y; +} + + +template +void +TestDef2::vector_value(const Point &p, + Vector & 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 +class TestDef3 : public Function +{ +private: + const double scale; + +public: + TestDef3(const unsigned int n_components, const double sc) + : Function(n_components) + , scale(sc) + {} + + virtual ~TestDef3() + {} + + virtual double + value(const Point &p, const unsigned int component = 0) const; + + void + vector_value(const Point &p, Vector &return_value) const; +}; + + +template +double +TestDef3::value(const Point &p, const unsigned int component) const +{ + double y = p(1); + + if (component == 0) + return scale * y; + else + return 0; +} + + +template +void +TestDef3::vector_value(const Point &p, + Vector & 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 +class TestPoly : public Function +{ +private: + std::vector> polys; + +public: + TestPoly(unsigned int deg) + : Function(2) + { + std::vector 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(coeff)); + } + } + + virtual ~TestPoly() + {} + + virtual double + value(const Point &p, const unsigned int component = 0) const; + + void + vector_value(const Point &p, Vector &return_value) const; +}; + + +template +double +TestPoly::value(const Point &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 +void +TestPoly::vector_value(const Point &p, + Vector & 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 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> this_value(n_q_points, + Vector(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 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 index 0000000000..adb1046f5d --- /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. +# +# +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. +# +# +-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. +# +# +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. +# +# +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. +# +# +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. +# +# +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. +# +# +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. +# +# +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. +# +# +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. +# +# +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. +# +# +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. +# +# +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. +# +# +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. +# +# +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. +# +# +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. +# +# +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. +# +# +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. +# +# +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. +# +# +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. +# +# +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. +# +# +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. +# +# +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. +# +# +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. +# +# +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. +# +# +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. +# +# +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. +# +# +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. +# +# +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. +# +# +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. +# +# +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. +# +# +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. +# +# +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. +# +# +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. +# +# +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. +# +# +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. +# +# +-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 index 0000000000..d54e39cc4f --- /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 +#include + +#include + +#include +#include +#include +#include +#include +#include +#include + +#include +#include + +#include + +#include + +#include "../tests.h" + + + +template +Tensor<1, dim> +ones() +{ + Tensor<1, dim> result; + for (unsigned int i = 0; i < dim; ++i) + result[i] = 1.0; + return result; +} + +template +void +test(const Triangulation &tr, + const FiniteElement &fe, + const double tolerance) +{ + DoFHandler dof(tr); + dof.distribute_dofs(fe); + + std::stringstream ss; + + deallog << "FE=" << fe.get_name() << std::endl; + + const QGauss quadrature(4); + FEValues fe_values(fe, + quadrature, + update_gradients | update_quadrature_points | + update_JxW_values); + + for (typename DoFHandler::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::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 +void +test_hyper_cube(const double tolerance) +{ + Triangulation tr; + GridGenerator::hyper_cube(tr); + + typename Triangulation::active_cell_iterator cell = tr.begin_active(); + for (unsigned int i = 0; i < GeometryInfo::vertices_per_cell; ++i) + { + Point &point = cell->vertex(i); + if (std::abs(point(dim - 1) - 1.0) < 1e-5) + point(dim - 1) += 0.15; + } + + FE_BernardiRaugel 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 index 0000000000..31a038b005 --- /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 -- 2.39.5