, Volume 40, Issue 1-3, pp 281-314

A Mixed DG Method for Linearized Incompressible Magnetohydrodynamics

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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 ℘ k 3 −℘ k−1 elements whereas the magnetic part of the equations is approximated by discontinuous ℘ k 3 −℘ 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.

D. Schötzau and X. Wei were supported in part by the Natural Sciences and Engineering Research Counsil of Canada (NSERC).