Adaptive Solution of a Singularly-Perturbed Convection-Diffusion Problem Using a Stabilized Mixed Finite Element Method

Abstract

We explore the applicability of a new adaptive stabilized dual-mixedfinite element method to a singularly-perturbed convection-diffusion equation withmixed boundary conditions. We establish the rate of convergence when the fluxand the concentration are approximated, respectively, by Raviart-Thomas/Brezzi-Douglas-Marini and continuous piecewise polynomials. We consider a simple a pos-teriori error indicator and provide some numerical experiments that illustrate theperformance of the method.