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A two-level discretization method for the stationary MHD equations. (English) Zbl 0898.76059

Summary: We analyze a two-level finite-element method for discretizing the equations of stationary, viscous, incompressible magnetohydrodynamics. We treat the equations under physically realistic (“nonideal”) boundary conditions that account for the electromagnetic interaction of the fluid with the surrounding media. The suggested algorithm involves solving a small, nonlinear problem on a coarse mesh and then one large, linear problem on a fine mesh. We prove well-posedness of the algorithm and optimal error estimates under a small-data assumption.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76W05 Magnetohydrodynamics and electrohydrodynamics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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