| Issue |
ESAIM: M2AN
Volume 42, Number 6, November-December 2008
|
|
|---|---|---|
| Page(s) | 1065 - 1087 | |
| DOI | https://doi.org/10.1051/m2an:2008034 | |
| Published online | 12 August 2008 | |
Convergent finite element discretizations of the nonstationary incompressible magnetohydrodynamics system
Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10,
72076 Tübingen, Germany. prohl@na.uni-tuebingen.de
Received:
10
March
2008
Revised:
24
June
2008
The incompressible MHD equations couple Navier-Stokes equations with Maxwell's equations
to describe the flow of a viscous, incompressible, and electrically conducting fluid in
a Lipschitz domain 
.
We verify convergence of iterates of different coupling and
decoupling fully discrete schemes towards weak solutions for
vanishing discretization parameters. Optimal first order of convergence is shown
in the presence of strong solutions for a splitting scheme which decouples
the computation of velocity field, pressure, and magnetic fields at
every iteration step.
Mathematics Subject Classification: 65N30
Key words: Magneto-hydrodynamics / discretization / FEM / fixed-point scheme / splitting-method.
© EDP Sciences, SMAI, 2008
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