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Houston, Paul; Schoetzau, Dominik; Wei, Xiaoxi
Publisher: Springer
Languages: English
Types: Article
Subjects:
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.
  • The results below are discovered through our pilot algorithms. Let us know how we are doing!

    • 10−2 C k h b10−4 − b k 10−6
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