An efficient two-level algorithm for the 2D/3D stationary incompressible magnetohydrodynamics based on the finite element method

In the paper, we develop a new two-level finite element algorithm for solving the 2D/3D stationary incompressible magnetohydrodynamics based on the Newton iterative method. This algorithm is consisting of solving one nonlinear system on a coarse mesh with mesh size H and two linearized problems with different loads on a fine mesh with mesh size h. Compared with existing work on the two-level method for the MHD model, our two-level method allows a much high order scaling between the coarse and fine grid sizes. Furthermore, stability and convergence of this present method are analyzed. Finally, the applicability and effectiveness of the present algorithm are illustrated by several numerical experiments.