Mixed upwinding covolume methods on rectangular grids for convection-diffusion problems

Abstract

We consider an upwinding covolume or control-volume method for a system of first order PDEs resulting from the mixed formulation of a convection-diffusion equation with a variable anisotropic diffusion tensor. The system can be used to model the steady state of the transport of a contaminant carried by a flow. We use the lowest order Raviart-Thomas space and show that the concentration and concentration flux both converge at one-half order provided that the exact flux is in H-1(Omega)(2) and the exact concentration is in H-1(Omega). Some numerical experiments illustrating the error behavior of the scheme are provided.