DISCONTINUOUS GALERKIN METHODS FOR ANISOTROPICSEMIDEFINITE DIFFUSION WITH ADVECTION

摘要

We construct and analyze a discontinuous Galerkin method to solve advection-diffusion-reaction PDEs with anisotropic and semidefinite diffusion. The method is designed toautomatically detect the so-called elliptic/hyperbolic interface on fitted meshes. The key idea is touse consistent weighted average and jump operators. Optimal estimates in the broken graph normare proven. These are consistent with well-known results when the problem is either hyperbolic oruniformly elliptic. The theoretical results are supported by numerical evidence.