Richardson extrapolation method for 2D-SPP on VB mesh singularly perturbed convection-diffusion problem on a Vulanovic-Bakhvalov mesh

This paper discusses the Richardson extrapolation technique of an upwind finite difference scheme on a modified Bakhvalov-type mesh (named Vulanovic-Bakhvalov mesh) for a model singularly perturbed convection-diffusion problem in two dimensions. We give a rigorous convergence analysis for the Richardson extrapolation method, which is shown that the use of Richardson extrapolation technique improves the epsilon-uniform accuracy of the presented scheme in the discrete maximum norm from O (N-1) to O (N-2), where N is the number of mesh-intervals. Then we also propose a new numerical method to obtain the optimization mesh parameters of the Vulanovic-Bakhvalov mesh. Finally some numerical experiments are provided to validate our theoretical results.