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A higher order numerical method for singularly perturbed elliptic problems with characteristic boundary layers (2311.00554v1)
Published 1 Nov 2023 in math.NA and cs.NA
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.