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Xiaoxi Wei
IAM M.Sc. Student, Department of Mathematics

DG-CG Finite Element Methods for an Incompressible Magneto-Hydrodynamic System

A mixed variational formulation for the equations of incompressible magneto-hydrodynamics is introduced and analyzed. Two finite element approximations are proposed, in which the hydrodynamic unknowns are discretized by standard inf-sup stable velocity-pressure pair, and the magnetic ones by either a mixed approach using Nedelec's elements of the first kind or a non-stabilized discontinuous Galerkin method. A priori error estimates in the energy norm are derived which show optimal convergence rates.

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