A Mixed Discontinuous Galerkin Method for Incompressible Magnetohydrodynamics

Houston, Paul; Schoetzau, Dominik; Wei, Xiaoxi

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.

Citation

Houston, P., Schoetzau, D., & Wei, X. A Mixed Discontinuous Galerkin Method for Incompressible Magnetohydrodynamics. Manuscript submitted for publication

• Journal Article Type: Article
• Deposit Date: Jun 9, 2008
• Journal: Journal of Scientific Computing
• Print ISSN: 0885-7474
• Publisher: Springer Verlag
• Peer Reviewed: Not Peer Reviewed
• Public URL: https://nottingham-repository.worktribe.com/output/1015874