From 3143a8e89cac1c17407d4881dcf729d333e16f0b Mon Sep 17 00:00:00 2001 From: wolf Date: Thu, 28 Jul 2005 22:54:54 +0000 Subject: [PATCH] Doc updates git-svn-id: https://svn.dealii.org/trunk@11213 0785d39b-7218-0410-832d-ea1e28bc413d --- deal.II/deal.II/include/numerics/vectors.h | 57 ++++++++++++---------- 1 file changed, 30 insertions(+), 27 deletions(-) diff --git a/deal.II/deal.II/include/numerics/vectors.h b/deal.II/deal.II/include/numerics/vectors.h index 6474e6381a..afa1f7112e 100644 --- a/deal.II/deal.II/include/numerics/vectors.h +++ b/deal.II/deal.II/include/numerics/vectors.h @@ -85,12 +85,15 @@ class ConstraintMatrix; * given function may be, taking into account that a virtual function has * to be called. * - *
  • Projection: compute the L2-projection of the given function onto - * the finite element space. This is done through the solution of the + *
  • Projection: compute the L2-projection of the given + * function onto the finite element space, i.e. if f is the function + * to be projected, compute fh in L2 such + * that (fh,vh)=(f,vh) for all discrete + * test functions vh. This is done through the solution of the * linear system of equations $M v = f$ where $M$ is the mass matrix * $m_{ij} = \int_\Omega \phi_i(x) \phi_j(x) dx$ and * $f_i = \int_\Omega f(x) \phi_i(x) dx$. The solution vector $v$ then is - * the projection. + * the nodal representation of the projection fh. * * In order to get proper results, it be may necessary to treat * boundary conditions right. Below are listed some cases where this @@ -223,19 +226,19 @@ class ConstraintMatrix; * function in different norms. The integration is performed using a given * quadrature formulae and assumes that the given finite element objects equals * that used for the computation of the solution. - * + * * The result is stored in a vector (named @p difference), where each entry * equals the given norm of the difference on a cell. The order of entries * is the same as a @p cell_iterator takes when started with @p begin_active and * promoted with the ++ operator. - * + * * You can use the @p distribute_cell_to_dof_vector function of the * DoFHandler class to convert cell based data to a data * vector with values on the degrees of freedom, which can then be * added to a DataOut object to be printed. But also you can * add a cell based data vector itself to a DataOut object, * see the @p DataOut::add_data_vector functions. - * + * * Presently, there is the possibility to compute the following values from the * difference, on each cell: @p mean, @p L1_norm, @p L2_norm, @p Linfty_norm, * @p H1_seminorm and @p H1_norm, see @p VectorTools::NormType. @@ -265,7 +268,7 @@ class ConstraintMatrix; * norm of the gradient of the difference. The square of the full * H1 norm is the sum of the square of seminorm * and the square of the L2 norm. - * + * * To get the global L1 error, you have to sum up the * entries in @p difference, e.g. using * Vector::l1_norm function. For the global L2 @@ -275,7 +278,7 @@ class ConstraintMatrix; * represent the $l_1$ and $l_2$ norms of the vectors, but you need * not take the absolute value of each entry, since the cellwise * norms are already positive. - * + * * To get the global mean difference, simply sum up the elements as above. * To get the $L_\infty$ norm, take the maximum of the vector elements, e.g. * using the Vector::linfty_norm function. @@ -370,9 +373,9 @@ class VectorTools * Linfty. */ W1infty_norm - + }; - + /** * Compute the interpolation of * @p function at the support @@ -399,7 +402,7 @@ class VectorTools const DoFHandler &dof, const Function &function, VECTOR &vec); - + /** * Calls the @p interpolate * function above with @@ -436,7 +439,7 @@ class VectorTools const FullMatrix &transfer, const InVector &data_1, OutVector &data_2); - + /** * Compute the projection of * @function to the finite element space. @@ -500,7 +503,7 @@ class VectorTools const bool enforce_zero_boundary = false, const Quadrature<0> &q_boundary = *invalid_face_quadrature, const bool project_to_boundary_first = false); - + /** * Calls the @p project * function, see above, with @@ -524,14 +527,14 @@ class VectorTools * * See the general documentation of this * class for further information. - */ + */ template static void create_right_hand_side (const Mapping &mapping, const DoFHandler &dof, const Quadrature &q, const Function &rhs, Vector &rhs_vector); - + /** * Calls the @p create_right_hand_side * function, see above, with @@ -574,7 +577,7 @@ class VectorTools const Function<1> &rhs, Vector &rhs_vector, const std::set &boundary_indicators = std::set()); - + /** * Calls the * @p create_boundary_right_hand_side @@ -587,7 +590,7 @@ class VectorTools const Function &rhs, Vector &rhs_vector, const std::set &boundary_indicators = std::set()); - + /** * Prepare Dirichlet boundary * conditions. Make up the list @@ -705,7 +708,7 @@ class VectorTools const Function<1> &boundary_function, std::map &boundary_values, const std::vector &component_mask = std::vector()); - + /** * Calls the other * @p interpolate_boundary_values @@ -731,7 +734,7 @@ class VectorTools std::map &boundary_values, const std::vector &component_mask = std::vector()); - + /** * Project @p function to the boundary * of the domain, using the given quadrature @@ -771,7 +774,7 @@ class VectorTools const FunctionMap<1>::type &boundary_functions, const Quadrature<0> &q, std::map &boundary_values); - + /** * Calls the @p project_boundary_values * function, see above, with @@ -782,7 +785,7 @@ class VectorTools const typename FunctionMap::type &boundary_function, const Quadrature &q, std::map &boundary_values); - + /** * Compute the error of the finite element solution. * Integrate the difference between @@ -877,7 +880,7 @@ class VectorTools const Function& exact_solution, Vector& difference, const Point& point); - + /** * Subtract the (algebraic) mean value * from a vector. This function is most @@ -913,7 +916,7 @@ class VectorTools */ static void subtract_mean_value(Vector &v, const std::vector &p_select); - + /** * Compute the mean value of one * component of the solution. @@ -946,7 +949,7 @@ class VectorTools const Quadrature &quadrature, const InVector &v, const unsigned int component); - + /** * Calls the @p compute_mean_value * function, see above, with @@ -986,11 +989,11 @@ class VectorTools * Exception */ DeclException0 (ExcNoComponentSelected); - + private: /** - * Null pointer used to - * denote invalid face + * Null pointer used to + * denote invalid face * quadrature formulas in 1d. */ static const Quadrature<0> * const invalid_face_quadrature; -- 2.39.5