Two-level Newton iterative method based on nonconforming finite element discretization for 2D/3D stationary MHD equations

In this paper, two-level Newton iterative method based on nonconforming finite element discretization is presented for solving 2D/3D stationary incompressible magneto-hydrodynamics equations. First, the Crouzeix–Raviart type element for the velocity, and the conforming finite element for the magnetic field and pressure. The main idea of the proposed method is to solve MHD system by m Newton iterations on a coarse mesh, once correction by Stokes iteration on a fine mesh. The proposed method can save more computational time than one level method on the fine mesh with the same convergence rate. Moreover, the technical analysis of stability and optimal error estimates for two-level Newton iterative method are given. Finally, the applicability and efficiency of our proposed algorithm are illustrated by several numerical experiments. © 2022 Elsevier Ltd