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

Date
2024
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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Description
Publisher
Elsevier
Citation
Applied Numerical Mathematics, 2024, 201,pp. 85-101
Collections
Mathematics & Statistics
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Hegarty_2024_Higher.pdf
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Keywords
convection-diffusion, Shishkin mesh, Petrov-Galerkin, higher order, Statistics, Mathematical sciences
ULRR Identifiers
https://researchrepository.ul.ie/handle/10344/15589
 https://doi.org/10.34961/researchrepository-ul.26075884
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Funding Information
Sustainable Development Goals
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Type
Article
Rights
https://creativecommons.org/licenses/by-nc-sa/4.0/
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