We propose and analyze a stabilized finite element method for the incompressible magnetohydrodynamic equations. The numerical results that we present show a good behavior of our approximation in experiments which are relevant from an industrial viewpoint. We explain in particular in the proof of our convergence theorem why it may be interesting to stabilize the magnetic equation as soon as the hydrodynamic diffusion is small and even if the magnetic diffusion is large. This observation is confirmed by our numerical tests.
@article{hal-00691696,
author = {Gerbeau, Jean-Fr\'ed\'eric},
title = {A stabilized finite element method for the incompressible magnetohydrodynamic equations},
journal = {HAL},
volume = {2000},
number = {0},
year = {2000},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00691696}
}
Gerbeau, Jean-Frédéric. A stabilized finite element method for the incompressible magnetohydrodynamic equations. HAL, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/hal-00691696/