A Finite Difference Scheme for Multidimensional Convection-Diffusion Equations

Abstract

In this paper a finite difference scheme is proposed for multidimensional convection-diffusion-reaction equations, particularly designed to treat the most interesting case of small diffusion. It is based closely on the work S¸endur and Neslitu¨rk (2011). Application of the method to multidimensional convection-diffusion-reaction equation is based on a simple splitting of the convection-diffusion-reaction equation and then joining their approximations obtained with S¸endur and Neslitu¨rk (2011). The method adapts very well to all regimes with continuous transitions from one regime to another. Numerical tests show good performance of the method and superiority with respect to well known stabilized finite element methods.