Alternating evolution discontinuous Galerkin methods for convection-diffusion equations

In this work, we propose a high order alternating evolution discontinuous Galerkin (AEDG) method to solve convection-diffusion equations. The difficulties related to numerical fluxes of DG methods for diffusion problems have been a major issue of investigation in the literature. The AEDG scheme presented here is based on an alternating evolution system for convection-diffusion equations, and therefore no numerical fluxes are needed in the scheme formulation. Moreover, the method is shown to be consistent, conservative and stable. Numerical experiments are provided to show the goodness of the proposed method.