Year: 2014
Author: Mei-Ling Sun, Shan Jiang
Advances in Applied Mathematics and Mechanics, Vol. 6 (2014), Iss. 5 : pp. 604–614
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 ε. In contrast with the conventional methods, our method is much more accurate and effective.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.2013.m488
Advances in Applied Mathematics and Mechanics, Vol. 6 (2014), Iss. 5 : pp. 604–614
Published online: 2014-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 11
Keywords: Multiscale basis functions singular perturbation boundary layer adaptively graded meshes.
Author Details
-
REDUCED MULTISCALE COMPUTATION ON ADAPTED GRID FOR THE CONVECTION-DIFFUSION ROBIN PROBLEM
Journal of Applied Analysis & Computation, Vol. 7 (2017), Iss. 4 P.1488
https://doi.org/10.11948/2017091 [Citations: 3]