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arXiv · 2311.00554

A higher order numerical method for singularly perturbed elliptic problems with characteristic boundary layers

Alan F. Hegarty·Eugene O'Riordan
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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.

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Alan F. Hegarty, Eugene O'Riordan. 2026-06-06. A higher order numerical method for singularly perturbed elliptic problems with characteristic boundary layers. https://arxiv.org/abs/2311.00554

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