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Research Article | Open Access

A weak Galerkin finite element method for parabolic singularly perturbed convection-diffusion equations on layer-adapted meshes

Suayip Toprakseven1( ), Seza Dinibutun2
Department of Mathematics, Yozgat Bozok University, Yozgat, Turkey
Department of Mathematics and Natural Sciences, International University of Kuwait, Ardiya, Kuwait
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Abstract

In this paper, we designed and analyzed a weak Galerkin finite element method on layer adapted meshes for solving the time-dependent convection-dominated problems. Error estimates for semi-discrete and fully-discrete schemes were presented, and the optimal order of uniform convergence has been obtained. A special interpolation was delicately designed based on the structures of the designed method and layer-adapted meshes. We provided various numerical examples to confirm the theoretical findings.

Keywords

time dependent singularly perturbed problemweak Galerkin methodsemi-discrete and fully discrete schemeslayer-adapted-meshes

References

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Electronic Research Archive
Volume 32 Issue 8,
August 2024
Pages 5033-5066
DOI: 10.3934/era.2024232

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Cite this article:
Toprakseven S, Dinibutun S. A weak Galerkin finite element method for parabolic singularly perturbed convection-diffusion equations on layer-adapted meshes. Electronic Research Archive, 2024, 32(8): 5033-5066. https://doi.org/10.3934/era.2024232

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Received: 17 July 2024
Revised: 17 August 2024
Accepted: 19 August 2024
Published: 22 August 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)