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A fitted finite element method for singularly perturbed elliptic problems with characteristic boundary layers

Date
2026-03-01
Abstract
A Petrov–Galerkin finite element method on a rectangular Shishkin mesh is constructed for a singularly perturbed elliptic problem in two space dimensions. The solution contains a regular boundary layer and two characteristic boundary layers. The test functions are taken to be a tensor product of exponential splines in one coordinate direction and hat functions in the other direction, which results in a stable higher (than first) order numerical method. The differential equation contains a zero order term. Compared to the case of no zero order term, the character of the exponential splines are more complicated and the associated pointwise error analysis relies more on the finite element formulation. Error bounds are given in a global pointwise norm. Numerical results are presented to illustrate the performance of the method.
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Description
Publisher
Elsevier
Citation
Journal of Computational and Applied Mathematics 474, 116971
Collections
MACSI - Mathematics Application Consortium for Science & Industry
Mathematics & Statistics
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Hegarty_2025_Fitted.pdf
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Keywords
shishkin mesh, shishkin mesh, higher order
ULRR Identifiers
https://hdl.handle.net/10344/31350
 https://doi.org/10.34961/18862
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Funding Information
Sustainable Development Goals
Type
Article
Rights
http://creativecommons.org/licenses/by-nc-sa/4.0/
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