A Mixed DG Method for Linearized Incompressible Magnetohydrodynamics
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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 ℘k3−℘k−1 elements whereas the magnetic part of the equations is approximated by discontinuous ℘k3−℘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.
KeywordsIncompressible magnetohydrodynamics Mixed finite element methods Discontinuous Galerkin methods
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