A Modified Weak Galerkin Finite Element Method for Singularly Perturbed Parabolic Convection-Diffusion-Reaction Problems
Year: 2023
Author: Suayip Toprakseven, Fuzheng Gao
Journal of Computational Mathematics, Vol. 41 (2023), Iss. 6 : pp. 1246–1280
Abstract
In this work, a modified weak Galerkin finite element method is proposed for solving second order linear parabolic singularly perturbed convection-diffusion equations. The key feature of the proposed method is to replace the classical gradient and divergence operators by the modified weak gradient and modified divergence operators, respectively. We apply the backward finite difference method in time and the modified weak Galerkin finite element method in space on uniform mesh. The stability analyses are presented for both semi-discrete and fully-discrete modified weak Galerkin finite element methods. Optimal order of convergences are obtained in suitable norms. We have achieved the same accuracy with the weak Galerkin method while the degrees of freedom are reduced in our method. Various numerical examples are presented to support the theoretical results. It is theoretically and numerically shown that the method is quite stable.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2203-m2021-0031
Journal of Computational Mathematics, Vol. 41 (2023), Iss. 6 : pp. 1246–1280
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 35
Keywords: The modified weak Galerkin finite element method Backward Euler method Parabolic convection-diffusion problems Error estimates.