From 4fe55cd8147edb6f834f2e988c962757755ce494 Mon Sep 17 00:00:00 2001 From: bangerth Date: Tue, 22 Feb 2011 17:58:28 +0000 Subject: [PATCH] Fix spelling. git-svn-id: https://svn.dealii.org/trunk@23417 0785d39b-7218-0410-832d-ea1e28bc413d --- deal.II/doc/doxygen/headers/vector_valued.h | 66 ++++++++++----------- 1 file changed, 33 insertions(+), 33 deletions(-) diff --git a/deal.II/doc/doxygen/headers/vector_valued.h b/deal.II/doc/doxygen/headers/vector_valued.h index 2f3126bde2..b1038513b9 100644 --- a/deal.II/doc/doxygen/headers/vector_valued.h +++ b/deal.II/doc/doxygen/headers/vector_valued.h @@ -34,7 +34,7 @@ *
  • Complex-valued solutions consisting of real and imaginary parts, as * discussed for example in step-29. * - * + * * This page gives an overview of how to implement such vector-valued problems * efficiently in deal.II. * @@ -218,7 +218,7 @@ * cells; this is done using the FE_DGQ class. The combined element will then * be described by * @code - * FESystem finite_element (FERaviartThomas(1), 1, + * FESystem finite_element (FE_RaviartThomas(1), 1, * FE_DGQ(1), 1); * @endcode * i.e. we combine a single copy of the Raviart-Thomas element with a single @@ -245,7 +245,7 @@ * * * @anchor VVAssembling - *

    Assembling linear systems

    + *

    Assembling linear systems

    * * The next step is to assemble the linear system. How to do this for the * simple case of a scalar problem has been shown in many tutorial programs, @@ -261,7 +261,7 @@ const FEValuesExtractors::Scalar pressure (dim); ... - + typename DoFHandler::active_cell_iterator cell = dof_handler.begin_active(), endc = dof_handler.end(); @@ -273,8 +273,8 @@ right_hand_side.value_list (fe_values.get_quadrature_points(), rhs_values); - - for (unsigned int q=0; q @@ -412,7 +412,7 @@ const FEValuesExtractors::Vector displacements (0); ... - + for (unsigned int q_point=0; q_point phi_j_grad = fe_values[displacements].gradient (j,q_point); const double phi_j_div = fe_values[displacements].divergence (j,q_point); - cell_matrix(i,j) + cell_matrix(i,j) += (lambda_values[q_point] * phi_i_div * phi_j_div + mu_values[q_point] * - scalar_product(phi_i_grad, phi_j_grad) + scalar_product(phi_i_grad, phi_j_grad) + mu_values[q_point] * scalar_product(phi_i_grad, transpose(phi_j_grad)) @@ -442,7 +442,7 @@ fe_values.JxW(q_point); } } - * @endcode + * @endcode * * The scalar product between two tensors used in this bilinear form is * implemented as follows: @@ -459,14 +459,14 @@ scalar_product (const Tensor<2,dim> &u, tmp += u[i][j] * v[i][j]; return tmp; } - * @endcode + * @endcode * * Now, this is not the code used in step-8. In fact, * if one used the above code over the one implemented in that program, * it would run about 8 per cent slower. It can be improved (bringing * down the penalty to about 4 per cent) by taking a close look at the * bilinear form. In fact, we can transform it as follows: -@f{eqnarray*} +@f{eqnarray*} a({\mathbf u}, {\mathbf v}) &=& \left( @@ -492,7 +492,7 @@ scalar_product (const Tensor<2,dim> &u, \sum_{i,j} \left( \mu \partial_i u_j, \frac 12[\partial_i v_j + \partial_j v_i] - \right)_\Omega + \right)_\Omega \\ &=& \left( @@ -533,15 +533,15 @@ scalar_product (const Tensor<2,dim> &u, = fe_values[displacements].symmetric_gradient (i,q_point); const double phi_i_div = fe_values[displacements].divergence (i,q_point); - - for (unsigned int j=0; j phi_j_symmgrad = fe_values[displacements].symmetric_gradient (j,q_point); const double phi_j_div = fe_values[displacements].divergence (j,q_point); - cell_matrix(i,j) + cell_matrix(i,j) += (phi_i_div * phi_j_div * lambda_values[q_point] + @@ -552,7 +552,7 @@ scalar_product (const Tensor<2,dim> &u, fe_values.JxW(q_point)); } } - * @endcode + * @endcode * * So if, again, this is not the code we use in step-8, what do * we do there? The answer rests on the finite element we use. There, we use the @@ -674,7 +674,7 @@ scalar_product (const Tensor<2,dim> &u, = \left( \begin{array}{c} F \\ G \end{array} - \right). + \right). @f} * What this system means, of course, is @f{eqnarray*} @@ -725,16 +725,16 @@ scalar_product (const Tensor<2,dim> &u, system_matrix.block(0,1).vmult (tmp, solution.block(1)); tmp *= -1; tmp += system_rhs.block(0); - + SolverControl solver_control (solution.block(0).size(), 1e-8*tmp.l2_norm()); SolverCG<> cg (solver_control, vector_memory); - + cg.solve (system_matrix.block(0,0), solution.block(0), tmp, - PreconditionIdentity()); + PreconditionIdentity()); * @endcode * * What's happening here is that we allocate a temporary vector with as many @@ -767,7 +767,7 @@ scalar_product (const Tensor<2,dim> &u, * @code std::vector > local_solution_values (n_q_points, Vector (dim+1)); - + typename DoFHandler::active_cell_iterator cell = dof_handler.begin_active(), endc = dof_handler.end(); @@ -800,8 +800,8 @@ scalar_product (const Tensor<2,dim> &u, Tensor<1,dim> velocity; for (unsigned int d=0; dTensor@<1,dim@> because the @@ -815,7 +815,7 @@ scalar_product (const Tensor<2,dim> &u, std::vector > local_velocity_values (n_q_points); const FEValuesExtractors::Vector velocities (0); - + typename DoFHandler::active_cell_iterator cell = dof_handler.begin_active(), endc = dof_handler.end(); @@ -842,7 +842,7 @@ scalar_product (const Tensor<2,dim> &u, std::vector local_pressure_values (n_q_points); const FEValuesExtractors::Scalar pressure (dim); - + typename DoFHandler::active_cell_iterator cell = dof_handler.begin_active(), endc = dof_handler.end(); @@ -924,7 +924,7 @@ scalar_product (const Tensor<2,dim> &u, data_out.add_data_vector (solution, solution_names, DataOut::type_dof_data, data_component_interpretation); - data_out.build_patches (); + data_out.build_patches (); * @endcode * In other words, we here create an array of dim+1 elements in * which we store which elements of the finite element are vectors and which @@ -936,8 +936,8 @@ scalar_product (const Tensor<2,dim> &u, * Visualization programs like Visit and Paraview will then offer to show * these dim components as vector fields, rather than as * individual scalar fields. - * - * + * + * * @ingroup feall feaccess */ - + -- 2.39.5