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.
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