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

Published online by Cambridge University Press:  10 March 2015

Yanping Chen ,
Haitao Leng  and
Li-Bin Liu
Yanping Chen*
Affiliation:
School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China
Haitao Leng
Affiliation:
School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China
Li-Bin Liu
Affiliation:
School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China Department of Mathematics and Computer Science, Chizhou College, Anhui 247000, China
*
*Corresponding author. Email: [email protected] (Y. P. Chen)
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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 (N−2) which is robust with respect to the two perturbation parameters. Numerical results are given that confirm the theoretical result.

Keywords

65N30Non-monotonesingularly perturbedconvection-diffusionBakhvalov-typetwo small parameters
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 7 , Issue 2 , April 2015 , pp. 196 - 206
Copyright
Copyright © Global-Science Press 2015 

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