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We devise and analyze a class of the primal discontinuous Galerkin methodsfor the magnetic advection-diffusion problems based on the weighted-residualapproach. In addition to the upwind stabilization, we find a new mechanismunder the vector case that provides more flexibility in constructing theschemes. For the more general Friedrichs system, we show the stability andoptimal error estimate, which boil down to two core ingredients -- the weightfunction and the special projection -- that contain information of advection.Numerical experiments are provided to verify the theoretical results.

Discontinuous Galerkin methods for magnetic advection-diffusion problems