A decoupling penalty finite element method for the stationary incompressible MagnetoHydroDynamics equation

In this paper, we give a penalty finite element method for the steady MHD equations. In this method, we decouple the MHD into two equations, one for the velocity and magnetic (u,B), the other for the pressure p. We prove the existence of the penalty method and the optimal error estimate. Then, we give the penalty finite element method for the MHD equations. The stability analysis shows our method is stable, and the error estimate shows our method has an optimal convergence order. Finally, we give some numerical results of exact solution equation and Hartmann flow. The numerical results show that our penalty finite element method is effect.