Streamline diffusion finite element method for stationary incompressible magnetohydrodynamics

In this article, a streamline diffusion finite element method is proposed and analyzed for stationary incompressible magnetohydrodynamics (MHD) equations. This method is stable for any combinations of velocity, pressure, and magnet finite element spaces, without requiring Ladyzenskaja‐Babu?ka‐Brezzi (LBB) condition. The well‐posedness and convergence (at optimal error rate) of this scheme are proved in terms of some conditions. Two numerical experiments are illustrated to validate our theoretical analysis and show the streamline diffusion finite element approach is effective for solving the MHD problems. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1877–1901, 2014