Convergence analysis of an upwind mixed element method for advection diffusion problems

We consider a upwinding mixed element method for a system of first order partial differential equations resulting from the mixed formulation of a general advection diffusion problem. The system can be used to model the transport of a contaminant carried by a flow. We use the lowest order Raviart–Thomas mixed finite element space. We show the first order convergence both for concentration and concentration flux in L2(Ω)L2(Ω).