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

journal contribution
posted on 2024-06-21, 10:32 authored by Alan F HegartyAlan F Hegarty, E. O’Riordan

A Petrov-Galerkin finite element method is constructed for a singu?larly perturbed elliptic problem in two space dimensions. The solution contains a regular boundary layer and two characteristic boundary lay?ers. 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 sta?ble parameter-uniform numerical method that achieves a higher order of convergence compared to upwinding on the same mesh.

History

Publication

Applied Numerical Mathematics, 2024, 201,pp. 85-101

Publisher

Elsevier

Rights

This is the author’s version of a work that was accepted for publication in Applied Numerical Mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Applied Numerical Mathematics, 2024, 201,pp. 85-101https://doi.org/10.1016/j.apnum.2024.02.014,

Department or School

  • Mathematics & Statistics

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