From f1d70238e960adfd2ae295b72664353e46d3691b Mon Sep 17 00:00:00 2001 From: Ralf Hartmann Date: Tue, 11 Oct 2005 14:27:35 +0000 Subject: [PATCH] Replace unsupported symbol &delta. git-svn-id: https://svn.dealii.org/trunk@11585 0785d39b-7218-0410-832d-ea1e28bc413d --- deal.II/deal.II/include/fe/fe_poly_tensor.h | 9 ++++----- .../doc/doxygen/headers/deal.II/glossary.h | 20 +++++++++---------- 2 files changed, 13 insertions(+), 16 deletions(-) diff --git a/deal.II/deal.II/include/fe/fe_poly_tensor.h b/deal.II/deal.II/include/fe/fe_poly_tensor.h index c0cf51b345..f4df8768b2 100644 --- a/deal.II/deal.II/include/fe/fe_poly_tensor.h +++ b/deal.II/deal.II/include/fe/fe_poly_tensor.h @@ -56,13 +56,12 @@ * *

Determining the correct basis

* - * In most cases, the set of desired node values Ni - * and the basis functions vj will not fulfil the - * interpolation condition Ni(vj) = - * δij. + * In most cases, the set of desired node values $N_i$ and the basis + * functions $v_j$ will not fulfil the interpolation condition + * $N_i(v_j) = \delta_{ij}$. * * The use of the membaer data #inverse_node_matrix allows to compute - * the basis vj automatically, after the node values + * the basis $v_j$ automatically, after the node values * for ech original basis function of the polynomial space have been * computed. * diff --git a/deal.II/doc/doxygen/headers/deal.II/glossary.h b/deal.II/doc/doxygen/headers/deal.II/glossary.h index f2dececb85..ce4596b0d7 100644 --- a/deal.II/doc/doxygen/headers/deal.II/glossary.h +++ b/deal.II/doc/doxygen/headers/deal.II/glossary.h @@ -41,11 +41,10 @@ *
@anchor GlossNodes Node values or node functionals
* *
It is customary to define a FiniteElement as a pair consisting - * of a local function space and a set of node values - * (Ni) on the mesh cells (usually defined on the - * @ref GlossReferenceCell "reference cell"). Then, the basis of the local - * function space is chosen such that Ni(vj) - * = δij, the Kronecker delta. + * of a local function space and a set of node values $N_i$ on the + * mesh cells (usually defined on the @ref GlossReferenceCell + * "reference cell"). Then, the basis of the local function space is + * chosen such that $N_i(v_j) = \delta_{ij}$, the Kronecker delta. * * This splitting has several advantages, concerning analysis as well * as implementation. For the analysis, it means that conformity with @@ -80,12 +79,11 @@ *
@anchor GlossShape Shape functions
The restriction of * the finite element basis functions to a single grid cell.
* - *
@anchor GlossSupport Support points
- *
Support points are by definition those points pi, - * such that for the shape functions vj holds - * vj(pi) = δij. Therefore, a - * finite element interpolation can be defined uniquely by the values in the - * support points. + *
@anchor GlossSupport Support points
Support points are + * by definition those points $p_i$, such that for the shape functions + * $v_j$ holds $v_j(p_i) = \delta_{ij}$. Therefore, a finite element + * interpolation can be defined uniquely by the values in the support + * points. * * Lagrangian elements fill the vector accessed by * FiniteElementBase::get_unit_support_points(), such that the -- 2.39.5