Superconvergence of a Mixed Covolume Method for Elliptic Problems

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 L ² 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. Supported by the National Natural Science Foundation of China under grant No. 10071044 and the Research Fund of Doctoral Program of High Education by State Education Ministry of China.