SDFEM for an elliptic singularly perturbed problem with two parameters

Abstract

© 2018, Istituto di Informatica e Telematica del Consiglio Nazionale delle Ricerche. A singularly perturbed problem with two small parameters in two dimensions is investigated. Using its discretization by a streamline-diffusion finite element method with piecewise bilinear elements on a Shishkin mesh, we analyze the superconvergence property of the method and suggest the choice of stabilization parameters to attain optimal error estimate in the corresponding streamline-diffusion norm. Numerical tests confirm our theoretical results.