Mixed finite element methods for stationary incompressible magneto–hydrodynamics

  • Authors:

  • Dominik Schötzau

  • Affiliations:

  • University of Basel, Department of Mathematics, Switzerland

  • Venue:
  • Numerische Mathematik
  • Year:
  • 2004

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Abstract

A new mixed variational formulation of the equations of stationary incompressible magneto–hydrodynamics is introduced and analyzed. The formulation is based on curl-conforming Sobolev spaces for the magnetic variables and is shown to be well-posed in (possibly non-convex) Lipschitz polyhedra. A finite element approximation is proposed where the hydrodynamic unknowns are discretized by standard inf-sup stable velocity-pressure space pairs and the magnetic ones by a mixed approach using Nédélec’s elements of the first kind. An error analysis is carried out that shows that the proposed finite element approximation leads to quasi-optimal error bounds in the mesh-size.