Return to search

p-FEM quadrature error analysis on tetrahedra

In this paper we consider the p-FEM for elliptic boundary value problems on tetrahedral meshes where the entries of the stiffness matrix are evaluated by numerical quadrature. Such a quadrature can be done by mapping the tetrahedron to a hexahedron via the Duffy transformation.
We show that for tensor product Gauss-Lobatto-Jacobi quadrature formulas with q+1=p+1 points in each direction and shape functions that are adapted to the quadrature formula, one again has discrete stability for the fully discrete p-FEM.
The present error analysis complements the work [Eibner/Melenk 2005] for the p-FEM on triangles/tetrahedra where it is shown that by adapting the shape functions to the quadrature formula, the stiffness matrix can be set up in optimal complexity.

Identiferoai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:18842
Date30 November 2007
CreatorsEibner, Tino, Melenk, Jens Markus
PublisherTechnische Universität Chemnitz
Source SetsHochschulschriftenserver (HSSS) der SLUB Dresden
LanguageEnglish
Detected LanguageEnglish
Typedoc-type:preprint, info:eu-repo/semantics/preprint, doc-type:Text
Rightsinfo:eu-repo/semantics/openAccess

Page generated in 0.0021 seconds