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