An H1 weak Galerkin mixed finite element method for Sobolev equation

In this paper, we present a new H1 weak Galerkin mixed finite element method for the Sobolev equation which includes the exact solution u and the intermediate solution p. In the H1 weak Galerkin method, we adopt the discontinuous finite elements Pk/Pk for the approximation solution pair (uh,ph) on finite element partitions consisting of arbitrary shape of polygons which are WG shape regular. We give the semi-discrete and full-discrete formulations which are proven to be stable and parameter-free and possess the optimal error estimates. Numerical experiments show the efficiency of our methods.