--- /dev/null
+# $Id: Makefile,v 1.4 2006/02/10 17:53:05 wolf Exp $
+
+
+# For the small projects Makefile, you basically need to fill in only
+# four fields.
+#
+# The first is the name of the application. It is assumed that the
+# application name is the same as the base file name of the single C++
+# file from which the application is generated.
+target = $(basename $(shell echo step-*.cc))
+
+# The second field determines whether you want to run your program in
+# debug or optimized mode. The latter is significantly faster, but no
+# run-time checking of parameters and internal states is performed, so
+# you should set this value to `on' while you develop your program,
+# and to `off' when running production computations.
+debug-mode = off
+
+
+# As third field, we need to give the path to the top-level deal.II
+# directory. You need to adjust this to your needs. Since this path is
+# probably the most often needed one in the Makefile internals, it is
+# designated by a single-character variable, since that can be
+# reference using $D only, i.e. without the parentheses that are
+# required for most other parameters, as e.g. in $(target).
+D = ../../
+
+
+# The last field specifies the names of data and other files that
+# shall be deleted when calling `make clean'. Object and backup files,
+# executables and the like are removed anyway. Here, we give a list of
+# files in the various output formats that deal.II supports.
+clean-up-files = *gmv *gnuplot *gpl *eps *pov
+
+
+
+
+#
+#
+# Usually, you will not need to change something beyond this point.
+#
+#
+# The next statement tell the `make' program where to find the
+# deal.II top level directory and to include the file with the global
+# settings
+include $D/common/Make.global_options
+
+
+# Since the whole project consists of only one file, we need not
+# consider difficult dependencies. We only have to declare the
+# libraries which we want to link to the object file, and there need
+# to be two sets of libraries: one for the debug mode version of the
+# application and one for the optimized mode. Here we have selected
+# the versions for 2d. Note that the order in which the libraries are
+# given here is important and that your applications won't link
+# properly if they are given in another order.
+#
+# You may need to augment the lists of libraries when compiling your
+# program for other dimensions, or when using third party libraries
+libs.g = $(lib-deal2-2d.g) \
+ $(lib-deal2-3d.g) \
+ $(lib-lac.g) \
+ $(lib-base.g)
+libs.o = $(lib-deal2-2d.o) \
+ $(lib-deal2-3d.o) \
+ $(lib-lac.o) \
+ $(lib-base.o)
+
+
+# We now use the variable defined above which switch between debug and
+# optimized mode to select the set of libraries to link with. Included
+# in the list of libraries is the name of the object file which we
+# will produce from the single C++ file. Note that by default we use
+# the extension .g.o for object files compiled in debug mode and .o for
+# object files in optimized mode (or whatever the local default on your
+# system is instead of .o).
+ifeq ($(debug-mode),on)
+ libraries = $(target).g.$(OBJEXT) $(libs.g)
+else
+ libraries = $(target).$(OBJEXT) $(libs.o)
+endif
+
+
+# Now comes the first production rule: how to link the single object
+# file produced from the single C++ file into the executable. Since
+# this is the first rule in the Makefile, it is the one `make' selects
+# if you call it without arguments.
+$(target) : $(libraries)
+ @echo ============================ Linking $@
+ @$(CXX) -o $@$(EXEEXT) $^ $(LIBS) $(LDFLAGS)
+
+
+# To make running the application somewhat independent of the actual
+# program name, we usually declare a rule `run' which simply runs the
+# program. You can then run it by typing `make run'. This is also
+# useful if you want to call the executable with arguments which do
+# not change frequently. You may then want to add them to the
+# following rule:
+run: $(target)
+ @echo ============================ Running $<
+ @./$(target)$(EXEEXT)
+
+
+# As a last rule to the `make' program, we define what to do when
+# cleaning up a directory. This usually involves deleting object files
+# and other automatically created files such as the executable itself,
+# backup files, and data files. Since the latter are not usually quite
+# diverse, you needed to declare them at the top of this file.
+clean:
+ -rm -f *.$(OBJEXT) *~ Makefile.dep $(target)$(EXEEXT) $(clean-up-files)
+
+
+# Since we have not yet stated how to make an object file from a C++
+# file, we should do so now. Since the many flags passed to the
+# compiler are usually not of much interest, we suppress the actual
+# command line using the `at' sign in the first column of the rules
+# and write the string indicating what we do instead.
+./%.g.$(OBJEXT) :
+ @echo ==============debug========= $(<F)
+ @$(CXX) $(CXXFLAGS.g) -c $< -o $@
+./%.$(OBJEXT) :
+ @echo ==============optimized===== $(<F)
+ @$(CXX) $(CXXFLAGS.o) -c $< -o $@
+
+
+# The following statement tells make that the rules `run' and `clean'
+# are not expected to produce files of the same name as Makefile rules
+# usually do.
+.PHONY: run clean
+
+
+# Finally there is a rule which you normally need not care much about:
+# since the executable depends on some include files from the library,
+# besides the C++ application file of course, it is necessary to
+# re-generate the executable when one of the files it depends on has
+# changed. The following rule to created a dependency file
+# `Makefile.dep', which `make' uses to determine when to regenerate
+# the executable. This file is automagically remade whenever needed,
+# i.e. whenever one of the cc-/h-files changed. Make detects whether
+# to remake this file upon inclusion at the bottom of this file.
+#
+# If the creation of Makefile.dep fails, blow it away and fail
+Makefile.dep: $(target).cc Makefile \
+ $(shell echo $D/*/include/*/*.h)
+ @echo ============================ Remaking $@
+ @$D/common/scripts/make_dependencies $(INCLUDE) -B. $(target).cc \
+ > $@ \
+ || (rm -f $@ ; false)
+ @if test -s $@ ; then : else rm $@ ; fi
+
+
+# To make the dependencies known to `make', we finally have to include
+# them:
+include Makefile.dep
+
+
--- /dev/null
+/* $Id: step-22.cc 15679 2008-01-24 23:28:37Z bangerth $ */
+/* Author: Wolfgang Bangerth, Texas A&M University, 2008 */
+
+/* $Id: step-22.cc 15679 2008-01-24 23:28:37Z bangerth $ */
+/* Version: $Name$ */
+/* */
+/* Copyright (C) 2008 by the deal.II authors */
+/* */
+/* This file is subject to QPL and may not be distributed */
+/* without copyright and license information. Please refer */
+/* to the file deal.II/doc/license.html for the text and */
+/* further information on this license. */
+
+
+
+#include <base/quadrature_lib.h>
+#include <base/logstream.h>
+#include <base/function.h>
+#include <base/utilities.h>
+
+#include <lac/block_vector.h>
+#include <lac/full_matrix.h>
+#include <lac/block_sparse_matrix.h>
+#include <lac/solver_cg.h>
+#include <lac/precondition.h>
+#include <lac/sparse_direct.h>
+
+#include <grid/tria.h>
+#include <grid/grid_generator.h>
+#include <grid/tria_accessor.h>
+#include <grid/tria_iterator.h>
+#include <grid/tria_boundary_lib.h>
+#include <grid/grid_tools.h>
+#include <grid/grid_refinement.h>
+
+#include <dofs/dof_handler.h>
+#include <dofs/dof_renumbering.h>
+#include <dofs/dof_accessor.h>
+#include <dofs/dof_tools.h>
+#include <dofs/dof_constraints.h>
+
+#include <fe/fe_q.h>
+#include <fe/fe_dgq.h>
+#include <fe/fe_system.h>
+#include <fe/fe_values.h>
+#include <fe/mapping_q1.h>
+#include <fe/mapping_c1.h>
+
+#include <numerics/vectors.h>
+#include <numerics/matrices.h>
+#include <numerics/data_out.h>
+#include <numerics/error_estimator.h>
+#include <numerics/solution_transfer.h>
+
+#include <fstream>
+#include <sstream>
+
+using namespace dealii;
+
+
+
+template <int dim>
+class StokesProblem
+{
+ public:
+ StokesProblem (const unsigned int degree);
+ void run ();
+
+ private:
+ void setup_dofs ();
+ void assemble_system ();
+ void solve ();
+ void output_results (const unsigned int refinement_cycle) const;
+ void refine_mesh ();
+
+ const unsigned int degree;
+
+ Triangulation<dim> triangulation;
+ FESystem<dim> fe;
+ DoFHandler<dim> dof_handler;
+
+ ConstraintMatrix hanging_node_constraints;
+
+ BlockSparsityPattern sparsity_pattern;
+ BlockSparseMatrix<double> system_matrix;
+
+ BlockVector<double> solution;
+ BlockVector<double> system_rhs;
+
+ boost::shared_ptr<SparseDirectUMFPACK> A_preconditioner;
+};
+
+
+
+
+
+template <int dim>
+class PressureBoundaryValues : public Function<dim>
+{
+ public:
+ PressureBoundaryValues () : Function<dim>(1) {}
+
+ virtual double value (const Point<dim> &p,
+ const unsigned int component = 0) const;
+};
+
+
+template <int dim>
+double
+PressureBoundaryValues<dim>::value (const Point<dim> &/*p*/,
+ const unsigned int /*component*/) const
+{
+ return 0;
+}
+
+
+
+template <int dim>
+class BoundaryValues : public Function<dim>
+{
+ public:
+ BoundaryValues () : Function<dim>(dim+1) {}
+
+ virtual double value (const Point<dim> &p,
+ const unsigned int component = 0) const;
+
+ virtual void vector_value (const Point<dim> &p,
+ Vector<double> &value) const;
+};
+
+
+template <int dim>
+double
+BoundaryValues<dim>::value (const Point<dim> &p,
+ const unsigned int component) const
+{
+ if (component == 0)
+ return (p[0] < 0 ? -1 : (p[0] > 0 ? 1 : 0));
+ return 0;
+}
+
+
+template <int dim>
+void
+BoundaryValues<dim>::vector_value (const Point<dim> &p,
+ Vector<double> &values) const
+{
+ for (unsigned int c=0; c<this->n_components; ++c)
+ values(c) = BoundaryValues<dim>::value (p, c);
+}
+
+
+
+template <int dim>
+class RightHandSide : public Function<dim>
+{
+ public:
+ RightHandSide () : Function<dim>(dim+1) {}
+
+ virtual double value (const Point<dim> &p,
+ const unsigned int component = 0) const;
+
+ virtual void vector_value (const Point<dim> &p,
+ Vector<double> &value) const;
+};
+
+
+template <int dim>
+double
+RightHandSide<dim>::value (const Point<dim> &p,
+ const unsigned int component) const
+{
+ return 0;
+}
+
+
+template <int dim>
+void
+RightHandSide<dim>::vector_value (const Point<dim> &p,
+ Vector<double> &values) const
+{
+ for (unsigned int c=0; c<this->n_components; ++c)
+ values(c) = RightHandSide<dim>::value (p, c);
+}
+
+
+
+
+
+
+template <int dim>
+Tensor<1,dim>
+extract_u (const FEValuesBase<dim> &fe_values,
+ const unsigned int i,
+ const unsigned int q)
+{
+ Tensor<1,dim> tmp;
+
+ const unsigned int component
+ = fe_values.get_fe().system_to_component_index(i).first;
+
+ if (component < dim)
+ tmp[component] = fe_values.shape_value (i,q);
+
+ return tmp;
+}
+
+
+
+template <int dim>
+double
+extract_div_u (const FEValuesBase<dim> &fe_values,
+ const unsigned int i,
+ const unsigned int q)
+{
+ const unsigned int component
+ = fe_values.get_fe().system_to_component_index(i).first;
+
+ if (component < dim)
+ return fe_values.shape_grad (i,q)[component];
+ else
+ return 0;
+}
+
+
+
+template <int dim>
+Tensor<2,dim>
+extract_grad_s_u (const FEValuesBase<dim> &fe_values,
+ const unsigned int i,
+ const unsigned int q)
+{
+ Tensor<2,dim> tmp;
+
+ const unsigned int component
+ = fe_values.get_fe().system_to_component_index(i).first;
+
+ if (component < dim)
+ {
+ const Tensor<1,dim> grad_phi_over_2 = fe_values.shape_grad (i,q) / 2;
+
+ for (unsigned int e=0; e<dim; ++e)
+ tmp[component][e] += grad_phi_over_2[e];
+ for (unsigned int d=0; d<dim; ++d)
+ tmp[d][component] += grad_phi_over_2[d];
+ }
+
+ return tmp;
+}
+
+
+
+template <int dim>
+double extract_p (const FEValuesBase<dim> &fe_values,
+ const unsigned int i,
+ const unsigned int q)
+{
+ const unsigned int component
+ = fe_values.get_fe().system_to_component_index(i).first;
+
+ if (component == dim)
+ return fe_values.shape_value (i,q);
+ else
+ return 0;
+}
+
+
+
+
+template <class Matrix, class Preconditioner>
+class InverseMatrix : public Subscriptor
+{
+ public:
+ InverseMatrix (const Matrix &m,
+ const Preconditioner &preconditioner);
+
+ void vmult (Vector<double> &dst,
+ const Vector<double> &src) const;
+
+ private:
+ const SmartPointer<const Matrix> matrix;
+ const Preconditioner &preconditioner;
+
+ mutable GrowingVectorMemory<> vector_memory;
+};
+
+
+template <class Matrix, class Preconditioner>
+InverseMatrix<Matrix,Preconditioner>::InverseMatrix (const Matrix &m,
+ const Preconditioner &preconditioner)
+ :
+ matrix (&m),
+ preconditioner (preconditioner)
+{}
+
+
+
+template <class Matrix, class Preconditioner>
+void InverseMatrix<Matrix,Preconditioner>::vmult (Vector<double> &dst,
+ const Vector<double> &src) const
+{
+ SolverControl solver_control (src.size(), 1e-6*src.l2_norm());
+ SolverCG<> cg (solver_control, vector_memory);
+
+ dst = 0;
+
+ try
+ {
+ cg.solve (*matrix, dst, src, preconditioner);
+ }
+ catch (std::exception &e)
+ {
+ Assert (false, ExcMessage(e.what()));
+ }
+}
+
+
+
+template <class Preconditioner>
+class SchurComplement : public Subscriptor
+{
+ public:
+ SchurComplement (const BlockSparseMatrix<double> &A,
+ const InverseMatrix<SparseMatrix<double>,Preconditioner> &Minv);
+
+ void vmult (Vector<double> &dst,
+ const Vector<double> &src) const;
+
+ private:
+ const SmartPointer<const BlockSparseMatrix<double> > system_matrix;
+ const SmartPointer<const InverseMatrix<SparseMatrix<double>,Preconditioner> > m_inverse;
+
+ mutable Vector<double> tmp1, tmp2;
+};
+
+
+
+template <class Preconditioner>
+SchurComplement<Preconditioner>::
+SchurComplement (const BlockSparseMatrix<double> &A,
+ const InverseMatrix<SparseMatrix<double>,Preconditioner> &Minv)
+ :
+ system_matrix (&A),
+ m_inverse (&Minv),
+ tmp1 (A.block(0,0).m()),
+ tmp2 (A.block(0,0).m())
+{}
+
+
+template <class Preconditioner>
+void SchurComplement<Preconditioner>::vmult (Vector<double> &dst,
+ const Vector<double> &src) const
+{
+ system_matrix->block(0,1).vmult (tmp1, src);
+ m_inverse->vmult (tmp2, tmp1);
+ system_matrix->block(1,0).vmult (dst, tmp2);
+}
+
+
+
+template <int dim>
+StokesProblem<dim>::StokesProblem (const unsigned int degree)
+ :
+ degree (degree),
+ triangulation (Triangulation<dim>::maximum_smoothing),
+ fe (FE_Q<dim>(degree+1), dim,
+ FE_Q<dim>(degree), 1),
+ dof_handler (triangulation)
+{}
+
+
+
+
+template <int dim>
+void StokesProblem<dim>::setup_dofs ()
+{
+ dof_handler.distribute_dofs (fe);
+ DoFRenumbering::component_wise (dof_handler);
+
+ hanging_node_constraints.clear ();
+ DoFTools::make_hanging_node_constraints (dof_handler,
+ hanging_node_constraints);
+ hanging_node_constraints.close ();
+
+ std::vector<unsigned int> dofs_per_component (dim+1);
+ DoFTools::count_dofs_per_component (dof_handler, dofs_per_component);
+ const unsigned int n_u = dofs_per_component[0] * dim,
+ n_p = dofs_per_component[dim];
+
+ std::cout << " Number of active cells: "
+ << triangulation.n_active_cells()
+ << std::endl
+ << " Number of degrees of freedom: "
+ << dof_handler.n_dofs()
+ << " (" << n_u << '+' << n_p <<')'
+ << std::endl;
+
+ const unsigned int
+ n_couplings = dof_handler.max_couplings_between_dofs();
+
+ system_matrix.clear ();
+
+ sparsity_pattern.reinit (2,2);
+ sparsity_pattern.block(0,0).reinit (n_u, n_u, n_couplings);
+ sparsity_pattern.block(1,0).reinit (n_p, n_u, n_couplings);
+ sparsity_pattern.block(0,1).reinit (n_u, n_p, n_couplings);
+ sparsity_pattern.block(1,1).reinit (n_p, n_p, n_couplings);
+
+ sparsity_pattern.collect_sizes();
+
+
+ DoFTools::make_sparsity_pattern (dof_handler, sparsity_pattern);
+ hanging_node_constraints.condense (sparsity_pattern);
+ sparsity_pattern.compress();
+
+ system_matrix.reinit (sparsity_pattern);
+
+ solution.reinit (2);
+ solution.block(0).reinit (n_u);
+ solution.block(1).reinit (n_p);
+ solution.collect_sizes ();
+
+ system_rhs.reinit (2);
+ system_rhs.block(0).reinit (n_u);
+ system_rhs.block(1).reinit (n_p);
+ system_rhs.collect_sizes ();
+}
+
+
+template <int dim>
+double
+scalar_product (const Tensor<2,dim> &a,
+ const Tensor<2,dim> &b)
+{
+ double tmp = 0;
+ for (unsigned int i=0; i<dim; ++i)
+ for (unsigned int j=0; j<dim; ++j)
+ tmp += a[i][j] * b[i][j];
+ return tmp;
+}
+
+
+
+template <int dim>
+void StokesProblem<dim>::assemble_system ()
+{
+ system_matrix=0;
+ system_rhs=0;
+
+ QGauss<dim> quadrature_formula(degree+2);
+ QGauss<dim-1> face_quadrature_formula(degree+2);
+
+ FEValues<dim> fe_values (fe, quadrature_formula,
+ update_values |
+ update_quadrature_points |
+ update_JxW_values |
+ update_gradients);
+ FEFaceValues<dim> fe_face_values (fe, face_quadrature_formula,
+ update_values | update_normal_vectors |
+ update_quadrature_points | update_JxW_values);
+
+ const unsigned int dofs_per_cell = fe.dofs_per_cell;
+
+ const unsigned int n_q_points = quadrature_formula.size();
+ const unsigned int n_face_q_points = face_quadrature_formula.size();
+
+ FullMatrix<double> local_matrix (dofs_per_cell, dofs_per_cell);
+ Vector<double> local_rhs (dofs_per_cell);
+
+ std::vector<unsigned int> local_dof_indices (dofs_per_cell);
+
+ const PressureBoundaryValues<dim> pressure_boundary_values;
+
+ std::vector<double> boundary_values (n_face_q_points);
+
+ typename DoFHandler<dim>::active_cell_iterator
+ cell = dof_handler.begin_active(),
+ endc = dof_handler.end();
+ for (; cell!=endc; ++cell)
+ {
+ fe_values.reinit (cell);
+ local_matrix = 0;
+ local_rhs = 0;
+
+ for (unsigned int q=0; q<n_q_points; ++q)
+ {
+ for (unsigned int i=0; i<dofs_per_cell; ++i)
+ {
+
+ const Tensor<1,dim> phi_i_u = extract_u (fe_values, i, q);
+
+ const Tensor<2,dim> phi_i_grads_u= extract_grad_s_u (fe_values, i, q);
+ const double div_phi_i_u = extract_div_u (fe_values, i, q);
+ const double phi_i_p = extract_p (fe_values, i, q);
+
+ for (unsigned int j=0; j<dofs_per_cell; ++j)
+ {
+ const Tensor<2,dim> phi_j_grads_u = extract_grad_s_u (fe_values, j, q);
+ const double div_phi_j_u = extract_div_u (fe_values, j, q);
+ const double phi_j_p = extract_p (fe_values, j, q);
+
+ local_matrix(i,j) += (scalar_product(phi_i_grads_u, phi_j_grads_u)
+ - div_phi_i_u * phi_j_p
+ - phi_i_p * div_phi_j_u
+ + phi_i_p * phi_j_p)
+ * fe_values.JxW(q);
+ }
+ }
+ }
+
+
+ for (unsigned int face_no=0;
+ face_no<GeometryInfo<dim>::faces_per_cell;
+ ++face_no)
+ if (cell->at_boundary(face_no))
+ {
+ fe_face_values.reinit (cell, face_no);
+
+ pressure_boundary_values
+ .value_list (fe_face_values.get_quadrature_points(),
+ boundary_values);
+
+ for (unsigned int q=0; q<n_face_q_points; ++q)
+ for (unsigned int i=0; i<dofs_per_cell; ++i)
+ {
+ const Tensor<1,dim>
+ phi_i_u = extract_u (fe_face_values, i, q);
+
+ local_rhs(i) += -(phi_i_u *
+ fe_face_values.normal_vector(q) *
+ boundary_values[q] *
+ fe_face_values.JxW(q));
+ }
+ }
+
+ cell->get_dof_indices (local_dof_indices);
+
+ for (unsigned int i=0; i<dofs_per_cell; ++i)
+ for (unsigned int j=0; j<dofs_per_cell; ++j)
+ system_matrix.add (local_dof_indices[i],
+ local_dof_indices[j],
+ local_matrix(i,j));
+
+ for (unsigned int i=0; i<dofs_per_cell; ++i)
+ system_rhs(local_dof_indices[i]) += local_rhs(i);
+ }
+
+ hanging_node_constraints.condense (system_matrix);
+ hanging_node_constraints.condense (system_rhs);
+
+ {
+ std::map<unsigned int,double> boundary_values;
+ std::vector<bool> component_mask (dim+1, true);
+ component_mask[dim] = false;
+ VectorTools::interpolate_boundary_values (dof_handler,
+ 3,
+ BoundaryValues<dim>(),
+ boundary_values,
+ component_mask);
+
+ MatrixTools::apply_boundary_values (boundary_values,
+ system_matrix,
+ solution,
+ system_rhs);
+ }
+
+ std::cout << " Computing preconditioner..." << std::flush;
+
+ A_preconditioner
+ = boost::shared_ptr<SparseDirectUMFPACK>(new SparseDirectUMFPACK());
+ A_preconditioner->initialize (system_matrix.block(0,0));
+
+ std::cout << std::endl;
+}
+
+
+
+template <int dim>
+void StokesProblem<dim>::solve ()
+{
+ const InverseMatrix<SparseMatrix<double>,SparseDirectUMFPACK>
+ A_inverse (system_matrix.block(0,0), *A_preconditioner);
+ Vector<double> tmp (solution.block(0).size());
+ Vector<double> schur_rhs (solution.block(1).size());
+
+ {
+ A_inverse.vmult (tmp, system_rhs.block(0));
+ system_matrix.block(1,0).vmult (schur_rhs, tmp);
+ schur_rhs -= system_rhs.block(1);
+
+ SchurComplement<SparseDirectUMFPACK>
+ schur_complement (system_matrix, A_inverse);
+
+ SolverControl solver_control (system_matrix.block(0,0).m(),
+ 1e-6*schur_rhs.l2_norm());
+ SolverCG<> cg (solver_control);
+
+ PreconditionSSOR<> preconditioner;
+ preconditioner.initialize (system_matrix.block(1,1), 1.2);
+
+ InverseMatrix<SparseMatrix<double>,PreconditionSSOR<> >
+ m_inverse (system_matrix.block(1,1), preconditioner);
+
+ try
+ {
+ cg.solve (schur_complement, solution.block(1), schur_rhs,
+ m_inverse);
+ }
+ catch (...)
+ {
+ abort ();
+ }
+
+ // produce a consistent flow field
+ hanging_node_constraints.distribute (solution);
+
+ std::cout << " "
+ << solver_control.last_step()
+ << " CG Schur complement iterations for pressure."
+ << std::endl;
+ }
+
+ {
+ system_matrix.block(0,1).vmult (tmp, solution.block(1));
+ tmp *= -1;
+ tmp += system_rhs.block(0);
+
+ A_inverse.vmult (solution.block(0), tmp);
+
+ // produce a consistent pressure field
+ hanging_node_constraints.distribute (solution);
+ }
+}
+
+
+
+template <int dim>
+void
+StokesProblem<dim>::output_results (const unsigned int refinement_cycle) const
+{
+ std::vector<std::string> solution_names (dim, "velocity");
+ solution_names.push_back ("p");
+
+ DataOut<dim> data_out;
+
+ data_out.attach_dof_handler (dof_handler);
+
+ std::vector<DataComponentInterpretation::DataComponentInterpretation>
+ data_component_interpretation
+ (dim+1, DataComponentInterpretation::component_is_scalar);
+ for (unsigned int i=0; i<dim; ++i)
+ data_component_interpretation[i]
+ = DataComponentInterpretation::component_is_part_of_vector;
+
+ data_out.add_data_vector (solution, solution_names,
+ DataOut<dim>::type_dof_data,
+ data_component_interpretation);
+
+ data_out.build_patches ();
+
+ std::ostringstream filename;
+ filename << "solution-"
+ << Utilities::int_to_string (refinement_cycle, 2)
+ << ".vtk";
+
+ std::ofstream output (filename.str().c_str());
+ data_out.write_vtk (output);
+}
+
+
+
+template <int dim>
+void
+StokesProblem<dim>::refine_mesh ()
+{
+ Vector<float> estimated_error_per_cell (triangulation.n_active_cells());
+
+ std::vector<bool> component_mask (dim+1, false);
+ component_mask[dim] = true;
+ KellyErrorEstimator<dim>::estimate (dof_handler,
+ QGauss<dim-1>(degree+1),
+ typename FunctionMap<dim>::type(),
+ solution,
+ estimated_error_per_cell,
+ component_mask);
+
+ GridRefinement::refine_and_coarsen_fixed_number (triangulation,
+ estimated_error_per_cell,
+ 0.3, 0.0);
+ triangulation.execute_coarsening_and_refinement ();
+}
+
+
+template <int dim>
+void StokesProblem<dim>::run ()
+{
+ switch (dim)
+ {
+ case 2:
+ {
+ std::vector<unsigned int> subdivisions (dim, 1);
+ subdivisions[0] = 4;
+
+ GridGenerator::subdivided_hyper_rectangle (triangulation,
+ subdivisions,
+ Point<dim>(-2,-1),
+ Point<dim>(2,0),
+ true);
+
+ triangulation.refine_global (2);
+
+ break;
+ }
+
+ case 3:
+ {
+ GridGenerator::hyper_shell (triangulation,
+ Point<dim>(), 0.5, 1.0);
+
+ static HyperShellBoundary<dim> boundary;
+ triangulation.set_boundary (0, boundary);
+
+ triangulation.refine_global (2);
+
+ break;
+ }
+
+ default:
+ Assert (false, ExcNotImplemented());
+ }
+
+
+ for (unsigned int refinement_cycle = 0; refinement_cycle<9;
+ ++refinement_cycle)
+ {
+ std::cout << "Refinement cycle " << refinement_cycle << std::endl;
+
+ if (refinement_cycle > 0)
+ refine_mesh ();
+
+ setup_dofs ();
+
+ std::cout << " Assembling..." << std::endl;
+ assemble_system ();
+
+ std::cout << " Solving..." << std::endl;
+ solve ();
+
+ output_results (refinement_cycle);
+
+ std::cout << std::endl;
+ }
+}
+
+
+
+int main ()
+{
+ try
+ {
+ deallog.depth_console (0);
+
+ StokesProblem<2> flow_problem(1);
+ flow_problem.run ();
+ }
+ catch (std::exception &exc)
+ {
+ std::cerr << std::endl << std::endl
+ << "----------------------------------------------------"
+ << std::endl;
+ std::cerr << "Exception on processing: " << std::endl
+ << exc.what() << std::endl
+ << "Aborting!" << std::endl
+ << "----------------------------------------------------"
+ << std::endl;
+
+ return 1;
+ }
+ catch (...)
+ {
+ std::cerr << std::endl << std::endl
+ << "----------------------------------------------------"
+ << std::endl;
+ std::cerr << "Unknown exception!" << std::endl
+ << "Aborting!" << std::endl
+ << "----------------------------------------------------"
+ << std::endl;
+ return 1;
+ }
+
+ return 0;
+}