THE DEFECT-CORRECTION TECHNIQUE APPLIED TO SINGULARLY PERTURBED ELLIPTIC PROBLEMS OF CONVECTION-DIFFUSION TYPE

Abstract. In this work the defect–correction technique is used to solve some singularly perturbed elliptic boundary value problems of convection-diffusion type. In [3] it was proved that the use of standard defect–correction technique allows one improve the order of convergence of stable low order finite difference schemes. Nevertheless, the analysis of the uniform convergence is difficult for 1D problems and at the moment we do not know of any theoretical result proving uniform convergence for general 2D elliptic prob-lems. In [4] a variant of this approach was proposed in order to simplify the analysis for 1D problems of convection-diffusion type, proving almost second order uniform con-vergence of the method. In this paper we show numerically that it is possible to extend the parameter-uniform method given in [4] to the case of a 2D elliptic boundary value problem