Finite element approximations of Green function Gx0ε based on the method of multiscale asymptotic expansions

On basis of He and Cui [W.-m. He, J.-z. Cui, A pointwise estimate on the 1-order approximation of Gx0ε, 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 Gx0ε defined in R2R2 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.