A Mixed Discontinuous Galerkin Method for Incompressible Magnetohydrodynamics - Houston, Paul; Schoetzau, Dominik; Wei, Xiaoxi (Springer, 2008)
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 P^3_{k}-P_{k-1} elements whereas the magnetic part of the equations is approximated by discontinuous P^3_{k}-P_{k+1} elements. We carry out a complete a-priori error analysis and prove that the energy norm error is convergent of order O(h^k) in the mesh size h. We also show that the method is able to correctly capture and resolve the strongest magnetic singularities in non-convex polyhedral domains. These results are verified in a series of numerical experiments.