From: Guido Kanschat Date: Thu, 22 Sep 2005 21:05:13 +0000 (+0000) Subject: text on node values X-Git-Tag: v8.0.0~13097 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=0739264da58d1fb34ae1aa87586dc28965c686ed;p=dealii.git text on node values git-svn-id: https://svn.dealii.org/trunk@11506 0785d39b-7218-0410-832d-ea1e28bc413d --- diff --git a/deal.II/doc/doxygen/headers/deal.II/glossary.h b/deal.II/doc/doxygen/headers/deal.II/glossary.h index 67f6994b39..35e455ae22 100644 --- a/deal.II/doc/doxygen/headers/deal.II/glossary.h +++ b/deal.II/doc/doxygen/headers/deal.II/glossary.h @@ -24,10 +24,55 @@ * and support points coincide. * * + *
@anchor GlossInterpolation Interpolation with finite elements
+ *
The purpose of interpolation with finite elements is computing + * a vector of coefficients representing a finite element function, + * such that the @ref GlossNodes "node values" of the original + * function and the finite element function coincide. Therefore, the + * interpolation process consists of evaluating all @ref GlossNodes + * "node functionals" Ni for the given function + * f and store the result as entry i in the coefficient + * vector. + * *
@anchor GlossLagrange Lagrange elements
*
Finite elements based on Lagrangian interpolation at * @ref GlossSupport "support points".
* + *
@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 + * @GlossReferenceCell "reference cell"). Then, the basis of the local + * function space is chosen such that Ni(vj) + * = δij, the Kronecker delta. + * + * This splitting has several advantages, concerning analysis as well + * as implementation. For the analysis, it means that conformity with + * certain spaces (FiniteElementData::Conformity), e.g. continuity, is + * up to the node values. In deal.II, it helps simplifying the + * implementation of more complex elements like FE_RaviartThomas + * considerably. + * + * Examples for node functionals are values in @ref GlossSupport + * "support points" and moments with respect to Legendre + * polynomials. Let us give some examples: + * + * + * + * + * + * + * + * + * + * + * + * + * + * + *
ElementFunction spaceNode values
FE_Q, FE_DGQQkvalues in support points
FE_DGPPkmoments with respect to Legendre polynomials
FE_RaviartThomas (2d)Qk+1,k x Qk,k+1moments on edges and in the interior
+ * *
@anchor GlossReferenceCell Reference cell
*
The hypercube [0,1]dim, on which all parametric finite * element shape functions are defined.