Discontinuous Galerkin methods for magnetic advection-diffusion problems

Abstract

We devise and analyze a class of the primal discontinuous Galerkin methods for magnetic advection-diffusion problems based on the weighted-residual approach. In addition to the upwind stabilization, we explore some terms related to convection under the vector case that provides more flexibility in constructing the schemes. Under a degenerate Friedrichs system, we show the stability and optimal error estimate, which boil down to two ingredients – the weight function and the special projection – that contain information of advection. Numerical experiments are provided to verify the theoretical results.