A Family of Characteristic Discontinuous Galerkin Methods for Transient Advection-Diffusion Equations and Their Optimal-Order L^2 Error Estimates

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 L 2 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. AMS subject classifications: 35R32, 37N30, 65M12, 76N15

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