Mixed Upwinding Covolume Methods on Rectangular Grids for Convection-Diffusion Problems

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 H1(Ω)2 and the exact concentration is in H1(Ω). Some numerical experiments illustrating the error behavior of the scheme are provided.