A singularly perturbed problem with two parameters in two dimensions on graded meshes

Abstract

© 2016 Elsevier Ltd A numerical approximation of a convection–reaction–diffusion problem by standard bilinear finite elements is considered. Using Duran–Lombardi and Duran–Shishkin type meshes we prove first order error estimates in an energy norm. Numerical examples confirm our theoretical results and show smaller errors compared to the well-known Shishkin mesh.