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Multiscale Basis Functions for Singular Perturbation on Adaptively Graded Meshes

Published online by Cambridge University Press:  03 June 2015

Mei-Ling Sun  and
Shan Jiang
Mei-Ling Sun
Affiliation:
College of Mathematics Science, Yangzhou University, Yangzhou 225002, China Education and Technology Center, Nantong Vocational College, Nantong 226007, China
Shan Jiang*
Affiliation:
College of Mathematics Science, Yangzhou University, Yangzhou 225002, China Department of Mathematics, Texas A&M University, College Station, TX 77843, USA
*
*Corresponding author. Email: jiangshan@yzu.edu.cn
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Abstract

We apply the multiscale basis functions for the singularly perturbed reaction-diffusion problem on adaptively graded meshes, which can provide a good balance between the numerical accuracy and computational cost. The multiscale space is built through standard finite element basis functions enriched with multiscale basis functions. The multiscale basis functions have abilities to capture originally perturbed information in the local problem, as a result our method is capable of reducing the boundary layer errors remarkably on graded meshes, where the layer-adapted meshes are generated by a given parameter. Through numerical experiments we demonstrate that the multiscale method can acquire second order convergence in the L2 norm and first order convergence in the energy norm on graded meshes, which is independent of ɛ. In contrast with the conventional methods, our method is much more accurate and effective.

Keywords

35J2565N1265N30Multiscale basis functionssingular perturbationboundary layeradaptively graded meshes
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 6 , Issue 5 , October 2014 , pp. 604 - 614
Copyright
Copyright © Global-Science Press 2014

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