Discretization of the Stationary Convection-Diffusion-Reaction Equation

In this paper we present a new finite volume discretization method based on an exponential flux approximation scheme. It can be applied to problems in which convective and diffusive terms, as well as a production term playa role; equations of this type are found among others in combustion theory. We show that the errors only depend on the variation of the coefficients within grid size, and not on the magnitude of local Peclet numbers. The scheme is shown to be second order accurate uniformly in Peclet numbers; which we believe to be unique for this method. Key words. convection-difFusion-reaction equation, finite volume method, flux computation. AMS subject classifications. Primary: 65N06, Secondary: 76M20, 65N12