A Family of Characteristic Discontinuous Galerkin Methods for TransientAdvection-Diffusion Equations and Their Optimal-Order L2 Error Estimates

Abstract. We develop a family of characteristic discontinuous Galerkin methods for transient advection-diffusion equations, including the characteristic NIPG, OBB, IIPG, and SIPG schemes. The derived schemes possess combined advantages of Eulerian-Lagrangian methods and discontinuous Galerkin methods. An optimal-order error estimate in the L2 norm and a superconvergence estimate in a weighted energy norm are proved for the characteristic NIPG, IIPG, and SIPG scheme. Numerical experi-ments are presented to confirm the optimal-order spatial and temporal convergence rates of these schemes as proved in the theorems and to show that these schemes com-pare favorably to the standard NIPG, OBB, IIPG, and SIPG schemes in the context of advection-diffusion equations