Abstract:

The purpose of this article is to develop and analyze least-squares
approximations for the incompressible magnetohydrodynamic equations. The major advantage of the least-squares finite element method is that it is not subjected to the so-called Ladyzhenskaya-Babuska-Brezzi (LBB) condition. The authors employ least-squares functionals which involve a discrete inner product which is related to the inner product in H^-1(\Omega).

Key words: The incompressible MHDs equation, negative norm, vorticity, least-squares mixed finite element method