Superconvergence analysis of a finite element method for a two-parameter singularly perturbed problem

Abstract

We consider a singularly perturbed elliptic problem with two small independent parameters and its discretization by a finite element method using piecewise bilinear elements on a layer-adapted mesh. We analyze superconvergence property of the method as well as a postprocessing technique which yields more accurate discrete solution. Numerical tests confirm our theoretical results.