Thomas Apel; Serge Nicaise; Joachim Schöberl : Crouzeix-Raviart type finite elements on anisotropic meshes

Author(s) :

Thomas Apel; Serge Nicaise; Joachim Schöberl

Title :

Crouzeix-Raviart type finite elements on anisotropic meshes

Electronic source :

[gzipped ps-file] 143 kB

Preprint series

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 99-13, 1999

Mathematics Subject Classification :

65N30 [ Finite numerical methods (BVP of PDE) ]

65N15 [ Error bounds (BVP of PDE) ]

65N50 [ Mesh generation and refinement (BVP of PDE) ]

65D05 [ Interpolation (numerical methods) ]

Abstract :

The paper deals with a non-conforming finite element method on a class of anisotropic meshes. The Crouzeix-Raviart element is used on triangles and tetrahedra. For rectangles and prismatic (pentahedral) elements a novel set of trial functions is proposed. Anisotropic local interpolation error estimates are derived for all these types of element and for functions from classical and weighted Sobolev spaces. The consistency error is estimated for a general differential equation under weak regularity assumptions. As a particular application, an example is investigated where anisotropic finite element meshes are appropriate, namely the Poisson problem in domains with edges. A numerical test is described.

Keywords :

Anisotropic mesh, Crouzeix-Raviart element, non-conforming finite element method, anisotropic interpolation error estimate, consistency error, edge singularity

Language :

english

Publication time :

5/1999