, Volume 96, Issue 4, pp 771-800

Mixed finite element methods for stationary incompressible magneto–hydrodynamics

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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.

Mathematics Subject Classification (2000): 65N30
This work was partially supported by the Swiss National Science Foundation under Project 2100-068126.02.