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Analysis of an unconditionally convergent stabilized finite element formulation for incompressible magnetohydrodynamics. (English) Zbl 1348.76097

Summary: In this work, we analyze a recently proposed stabilized finite element formulation for the approximation of the resistive magnetohydrodynamics equations. The novelty of this formulation with respect to existing ones is the fact that it always converges to the physical solution, even when it is singular. We have performed a detailed stability and convergence analysis of the formulation in a simplified setting. From the convergence analysis, we infer that a particular type of meshes with a macro-element structure is needed, which can be easily obtained after a straight modification of any original mesh.

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
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs

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