Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4629302 | Applied Mathematics and Computation | 2013 | 10 Pages |
Abstract
In this paper we provide three benchmark problems with known exact solutions that can be used to assess the ability of adaptive finite element algorithms to handle anisotropically-behaved solutions. The first one is a Poisson equation with a smooth solution that only changes in one spatial direction. The second one is a singularly-perturbed linear elliptic equation whose solution exhibits a boundary layer, and the last one is a two-equation system that contains a boundary layer in one solution component only. In an appendix we show sample results obtained with the open source library Hermes. (http://hpfem.org/hermes.)
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Pavel Solin, Ondrej Certik, Lukas Korous,