Application of generalized Gauss-Radau projections for the local discontinuous Galerkin method for linear convection-diffusion equations

In this paper we consider the local discontinuous Galerkin method based on the generalized alternating numerical fluxes, for solving the linear convection-diffusion equations in one dimension and two dimensions. As an application of generalized Gauss–Radau projections, we get rid of the dual argument and obtain directly the optimal L2-norm error estimate in a uniform framework. The sharpness of the theoretical results is demonstrated by numerical experiments.