Two-level Newton iterative method based on nonconforming finite element discretization for 2D/3D stationary MHD equations. (30th April 2022) - Xu, Jiali; Feng, Xinlong; Su, Haiyan
Abstract: 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. Highlights: A two-level nonconforming FEM was proposed for the 2D/3D MHD equations, which provide a reference on numerical methods to relate research. The proposed method improves computational efficiency than one level method on a fine mesh. The technical analysis of error estimates for our presented method is given. Numerical results show that our proposed method has some advantages over other methods in terms of error, convergence order and CPU time.