๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

The finite element method with anisotropic mesh grading for elliptic problems in domains with corners and edges

โœ Scribed by Thomas Apel; Serge Nicaise

Publisher
John Wiley and Sons
Year
1998
Tongue
English
Weight
574 KB
Volume
21
Category
Article
ISSN
0170-4214

No coin nor oath required. For personal study only.

โœฆ Synopsis

This paper is concerned with a specific finite element strategy for solving elliptic boundary value problems in domains with corners and edges. First, the anisotropic singular behaviour of the solution is described. Then the finite element method with anisotropic, graded meshes and piecewise linear shape functions is investigated for such problems; the schemes exhibit optimal convergence rates with decreasing mesh size. For the proof, new local interpolation error estimates for functions from anisotropically weighted spaces are derived. Finally, a numerical experiment is described, that shows a good agreement of the calculated approximation orders with the theoretically predicted ones. 1998

๐Ÿ“œ SIMILAR VOLUMES

Singularities of the Laplacian at corner
Singularities of the Laplacian at corners and edges of three-dimensional domains and their treatment with finite element methods
โœ E. Stephan; J. R. Whiteman ๐Ÿ“‚ Article ๐Ÿ“… 1988 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 475 KB

## Communicated by W. Wendland Three-dimensional Poisson problems containing boundary singularities are treated. The forms of the solutions for certain problems of this type are derived, where the domains of the problems can be represented in terms either of sphericalor of cylindrical-polar co-ord