Finite element approximations of Green function [formula omitted] based on the method of multiscale asymptotic expansions

Abstract

On basis of He and Cui [W.-m. He, J.-z. Cui, A pointwise estimate on the 1-order approximation of G x 0 ε , IMA Journal of Applied Mathematics 70 (2005) 241–269.], we propose two kinds of effective finite element algorithms to obtain numerical approximations of Green function G x 0 ε defined in R 2 based on the method of multiscale asymptotic expansions; we present their pointwise error estimates and analyse their computer memory and CPU time; finally, we report results from numerical experiments.