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A Mixed Discontinuous Galerkin Method for Incompressible Magnetohydrodynamics

Houston, Paul; Schoetzau, Dominik; Wei, Xiaoxi

Authors

Paul Houston Paul.Houston@nottingham.ac.uk

Dominik Schoetzau schoetzau@math.ubc.ca

Xiaoxi Wei weixiaoxi@math.ubc.ca



Abstract

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.

Journal Article Type Article
Journal Journal of Scientific Computing
Print ISSN 0885-7474
Publisher Humana Press
Peer Reviewed Not Peer Reviewed
APA6 Citation Houston, P., Schoetzau, D., & Wei, X. A Mixed Discontinuous Galerkin Method for Incompressible Magnetohydrodynamics. Manuscript submitted for publication
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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