A stabilized finite element method for the incompressible magnetohydrodynamic equations

We propose and analyze a stabilized finite element method for the incompres sible 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 eq uation as soon as the hydrodynamic diffusion is small and even if the magne tic diffusion is large. This observation is confirmed by our numerical test s. Mathematics Subject Classification (1991): 76W05, 65M12, 65M60.