Superconvergence of a Mixed Covolume Method for Elliptic Problems

Abstract

We consider a mixed covolume method for a system of first order partial differential equations resulting from the mixed formulation of a general self-adjoint elliptic problem with a variable full diffusion tensor. 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 in L2 norm and the superconvergence in certain discrete norms both for the pressure and velocity. Finally some numerical examples illustrating the error behavior of the scheme are provided.