A higher order numerical method for singularly perturbed elliptic problems with characteristic boundary layers
Numerical Analysis
2023-11-02 v1 Numerical Analysis
Abstract
A Petrov-Galerkin finite element method is constructed for a singularly perturbed elliptic problem in two space dimensions. The solution contains a regular boundary layer and two characteristic boundary layers. Exponential splines are used as test functions in one coordinate direction and are combined with bilinear trial functions defined on a Shishkin mesh. The resulting numerical method is shown to be a stable parameter-uniform numerical method that achieves a higher order of convergence compared to upwinding on the same mesh.
Cite
@article{arxiv.2311.00554,
title = {A higher order numerical method for singularly perturbed elliptic problems with characteristic boundary layers},
author = {Alan F. Hegarty and Eugene O'Riordan},
journal= {arXiv preprint arXiv:2311.00554},
year = {2023}
}
Comments
27 pages, 3 figures