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Fitted finite element methods for singularly perturbed elliptic problems of convection-diffusion type

journal contribution
posted on 2024-06-21, 08:37 authored by Alan F HegartyAlan F Hegarty, E. O’Riordan

Fitted finite element methods are constructed for a singularly perturbed convection-diffusion problem in two space dimensions. Exponential splines as basis functions are combined with Shishkin meshes to obtain a stable parameter-uniform numerical method. These schemes satisfy a discrete maximum principle. If the diffusivity parameter is bounded below by some fixed positive constant, the numerical approximations converge, in𝐿∞, at a rate of second order. Moreover, the numerical approximations converge at a rate of first order for all values of the singular perturbation parameter.


History

Publication

Applied Numerical Mathematics, 2024, 196, pp. 183-198

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, 196, pp. 183-198, https://doi.org/10.1016/j.apnum.2023.11.002

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  • Mathematics & Statistics

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