Error Analysis for a Non-Monotone FEM for a Singularly Perturbed Problem with Two Small Parameters. Issue 2 (April 2015)

• Record Type: Journal Article
• Authors: Chen, Yanping; Leng, Haitao; Liu, Li-Bin
• Is Part Of: Advances in applied mathematics and mechanics. Volume 7:Issue 2(2015)
• Page Start: 196
• Page End: 206
• Publication Date: 2015-04
• Subjects: 65N30; Non-monotone, -- singularly perturbed, -- convection-diffusion, -- Bakhvalov-type, -- two small parameters; Engineering mathematics -- Periodicals; Mechanics -- Periodicals; 620.00151825
• DOI: 10.4208/aamm.2013.m399
• Languages: English
• ISSNs: 2070-0733

Abstract

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.