A Mixed DG Method for Linearized Incompressible Magnetohydrodynamics

We introduce and analyze a discontinuous Galerkin method for the numerical discretization of a stationary incompressible magnetohydrodynamics model problem. The fluid unknowns are discretized with inf-sup stable discontinuous P3 k −Pk−1 elements whereas the magnetic part of the equations is approximated by discontinuous P3 k−Pk+1 elements. We carry out a complete a-priori error analysis of the method and prove that the energy norm error is optimally convergent in the mesh size. These results are verified in a series of numerical experiments.