Error Analysis for a Non-Monotone FEM for a Singularly Perturbed Problem with Two Small Parameters
Year: 2015
Author: Yanping Chen, Haitao Leng, Li-Bin Liu
Advances in Applied Mathematics and Mechanics, Vol. 7 (2015), Iss. 2 : pp. 196–206
Abstract
In this paper, we consider a singularly perturbed convection-diffusion problem. The problem involves two small parameters that gives rise to two boundary layers at two endpoints of the domain. For this problem, a non-monotone finite element methods is used. A priori error bound in the maximum norm is obtained. Based on the a priori error bound, we show that there exists Bakhvalov-type mesh that gives optimal error bound of $\mathcal{O}(N^{−2})$ which is robust with respect to the two perturbation parameters. Numerical results are given that confirm the theoretical result.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.2013.m399
Advances in Applied Mathematics and Mechanics, Vol. 7 (2015), Iss. 2 : pp. 196–206
Published online: 2015-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 11
Author Details
Yanping Chen Email
Haitao Leng Email
Li-Bin Liu Email
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https://doi.org/10.3934/era.2022109 [Citations: 0]