A Mixed DG Method for Linearized Incompressible Magnetohydrodynamics

Authors:
Paul Houston;Dominik Schötzau;Xiaoxi Wei
Affiliations:
School of Mathematical Sciences, University of Nottingham, Nottingham, UK NG7 2RD;Department of Mathematics, University of British Columbia, Vancouver, Canada V6T 1Z2;Department of Mathematics, University of British Columbia, Vancouver, Canada V6T 1Z2
Venue:
Journal of Scientific Computing
Year:
2009

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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 驴 k 3 驴驴 k驴1 elements whereas the magnetic part of the equations is approximated by discontinuous 驴 k 3 驴驴 k+1 elements. We carry out a complete a-priori error analysis of the method and prove that the energy norm error is convergent of order k in the mesh size. These results are verified in a series of numerical experiments.