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, Babu ka and Baumann [1], 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.