Discontinuous Galerkin methods for convection-diffusion equations with varying and vanishing diffusivity, Int

Abstract. This work formulates and analyzes a new family of discontinuous Galerkin methods for the time-dependent convection-diffusion equation with highly varying diffusion coefficients, that do not require the use of slope limit-ing techniques. The proposed methods are based on the standard NIPG/SIPG techniques, but use special diffusive numerical fluxes at some important inter-faces. The resulting numerical solutions have an L2 error that is significantly smaller than the error obtained with standard discontinuous Galerkin methods. Theoretical convergence results are also obtained