Finite element approximation of reaction–diffusion problems using an exponentially graded mesh

Abstract

We present the analysis of an h version Finite Element Method for the approximation of the solution to singularly perturbed reaction–diffusion problems posed in smooth domains Ω⊂R2. The method uses piecewise polynomials of degree p in each variable, defined on an exponentially graded mesh, optimally constructed for the approximation of exponential layers. We establish robust, optimal convergence rates in a variety of norms and illustrate our theoretical findings through numerical computations.