Abstract
In this paper, we consider the penalty based finite element methods for the 2D/3D stationary incompressible magnetohydrodynamics (MHD) equations with different Reynolds numbers. Penalty method is applied to address the incompressible constraint “ $$div \,\mathbf{u }=0$$ ” based on two different finite element pairs $$P_{1}{-}P_{0}{-}P_{1}$$ and $$P_{1}b{-}P_{1}{-}P_{1}b$$ . Furthermore, the proposed methods are the interesting combination of three different iterations and two-level finite element algorithm such that the uniqueness condition holds. Besides, the rigorous analysis of stability and optimal error estimate with respect to the penalty parameter $$\epsilon $$ for the proposed methods are given. Extensive 2D/3D numerical tests demonstrated the competitive performance of penalty methods.
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