A Mixed Discontinuous Galerkin Method for Incompressible Magnetohydrodynamics

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Houston, Paul ; Schoetzau, Dominik ; Wei, Xiaoxi
  • Publisher: Springer

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.
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    10−2 C k h b10−4 − b k 10−6

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