A Family of Characteristic Discontinuous Galerkin Methods for Transient Advection-Diffusion Equations and Their Optimal-Order L2 Error Estimates (Communications in Computational Physics, 2009)
We develop a family of characteristic discontinuous Galerkin methods fortransient advection-diffusion equations, including the characteristic NIPG, OBB, IIPG,and SIPG schemes. The derived schemes possess combined advantages of Eulerian-Lagrangianmethods and discontinuous Galerkin methods. An optimal-order errorestimate in the L2 norm and a superconvergence estimate in a weighted energy normare proved for the characteristic NIPG, IIPG, and SIPG scheme. Numerical experimentsare presented to confirm the optimal-order spatial and temporal convergencerates of these schemes as proved in the theorems and to show that these schemes comparefavorably to the standard NIPG, OBB, IIPG, and SIPG schemes in the context ofadvection-diffusion equations.