Convergent finite element discretization of the multi-fluid nonstationary incompressible magnetohydrodynamics equations

Baňas, Ľubomír; Prohl, Andreas

doi:10.1090/S0025-5718-10-02341-0

Convergent finite element discretization of the multi-fluid nonstationary incompressible magnetohydrodynamics equations
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by Ľubomír Baňas and Andreas Prohl;

Math. Comp. 79 (2010), 1957-1999

DOI: https://doi.org/10.1090/S0025-5718-10-02341-0

Published electronically: April 21, 2010

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Abstract:

We propose a convergent implicit stabilized finite element discretization of the nonstationary incompressible magnetohydrodynamics equations with variable density, viscosity, and electric conductivity. The discretization satisfies a discrete energy law, and a discrete maximum principle for the positive density, and iterates converge to weak solutions of the limiting problem for vanishing discretization parameters. A simple fixed point scheme, together with an appropriate stopping criterion is proposed, which decouples the computation of density, velocity, and magnetic field, and inherits the above properties, provided a mild mesh constraint holds. Computational studies are provided.

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