A Priori Error Analyses of a Stabilized Discontinuous Galerkin Method

We introduce a new stabilized discontinuous Galerkin method within a new function space setting, that is closely related to the discontinuous Galerkin formulation by Oden, Babuška and Baumann, but involves an extra stabilization term on the jumps of the normal fluxes across the element interfaces. The formulation satisfies a local conservation property and we prove well posedness of the new formulation. A priori error estimates are derived, which are verified by 1D and 2D experiments on a reaction-diffusion type model problem.