A Mixed Discontinuous Galerkin Method for Incompressible Magnetohydrodynamics

Houston, Paul and Schoetzau, Dominik and Wei, Xiaoxi (2008) A Mixed Discontinuous Galerkin Method for Incompressible Magnetohydrodynamics. Journal of Scientific Computing . (Submitted)

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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.

Item Type:Article
Schools/Departments:Faculty of Science > School of Mathematical Sciences
ID Code:912
Deposited By:Houston, Paul
Deposited On:09 Jun 2008 10:04
Last Modified:23 Jun 2011 08:07

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