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


Authors: Lubomír Banas and Andreas Prohl
Journal: Math. Comp. 79 (2010), 1957-1999
MSC (2010): Primary 65M60, 65M12, 76W05; Secondary 65M55, 65M50
DOI: https://doi.org/10.1090/S0025-5718-10-02341-0
Published electronically: April 21, 2010
MathSciNet review: 2684352
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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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Additional Information

Lubomír Banas
Affiliation: Department of Mathematics and the Maxwell Institute for Mathematical Sciences, Heriot-Watt University, EH14 4AS Edinburgh, United Kingdom
Email: l.banas@hw.ac.uk

Andreas Prohl
Affiliation: Mathematisches Institut der Universität Tübingen, Auf der Morgenstelle 10, D-72076 Tübingen, Germany
Email: prohl@na.uni-tuebingen.de

DOI: https://doi.org/10.1090/S0025-5718-10-02341-0
Received by editor(s): December 4, 2008
Received by editor(s) in revised form: August 7, 2009
Published electronically: April 21, 2010
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.