Error Analysis for a Non-Monotone FEM for a Singularly Perturbed Problem with Two Small Parameters

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

Keywords:   

Author Details

Yanping Chen

Haitao Leng

Li-Bin Liu

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