Iterative methods in penalty finite element discretization for the steady MHD equations

This paper characterizes one penalty finite element method for the incompressible MHD equations. The method is an interesting combination of the classic iterative schemes (Stokes, Newton and Oseen iterations) with two different finite element pairs P1bP1b–P1P1–P1bP1b and P1P1–P0P0–P1P1. Moreover, the rigorous analysis of stability and error estimate for the proposed methods are given. Finally, the applicability and effectiveness of the presented schemes are illustrated in several numerical experiments.