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Convergent finite element discretizations of thenonstationary incompressible magnetohydrodynamics system

Published online by Cambridge University Press:  12 August 2008

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

The incompressible MHD equations couple Navier-Stokes equations with Maxwell's equationsto describe the flow of a viscous, incompressible, and electrically conducting fluid ina Lipschitz domain $\Omega \subset \mathbb{R}^3$ .We verify convergence of iterates of different coupling anddecoupling fully discrete schemes towards weak solutions forvanishing discretization parameters. Optimal first order of convergence is shown in the presence of strong solutions for a splitting scheme which decouplesthe computation of velocity field, pressure, and magnetic fields atevery iteration step.

Keywords

Magneto-hydrodynamicsdiscretizationFEMfixed-point schemesplitting-method.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 42 , Issue 6 , November 2008 , pp. 1065 - 1087
Copyright
© EDP Sciences, SMAI, 2008

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