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The hp finite element method for singularly perturbed problems in nonsmooth domains

✍ Scribed by Christos Xenophontos

Publisher
John Wiley and Sons
Year
1999
Tongue
English
Weight
507 KB
Volume
15
Category
Article
ISSN
0749-159X

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✦ Synopsis

We consider the numerical approximation of singularly perturbed elliptic boundary value problems over nonsmooth domains. We use a decomposition of the solution that contains a smooth part, a corner layer part and a boundary layer part. Explicit guidelines for choosing mesh-degree combinations are given that yield finite element spaces with robust approximation properties. In particular, we construct an hp finite element space that approximates all components uniformly, at a near exponential rate.

πŸ“œ SIMILAR VOLUMES

The finite element method with anisotrop
The finite element method with anisotropic mesh grading for elliptic problems in domains with corners and edges
✍ Thomas Apel; Serge Nicaise πŸ“‚ Article πŸ“… 1998 πŸ› John Wiley and Sons 🌐 English βš– 574 KB

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