Error correction iterative finite element method based on charge‐conservative for the stationary inductionless magnetohydrodynamic system

Abstract In this paper, we propose and analyze a new error correction iterative finite element method (FEM) based on charge‐conservative for solving the stationary inductionless magnetohydrodynamic (MHD). The method consists of first solving the inductionless MHD equations by the Oseen iterative scheme to obtain an approximate solution, and then an error correction strategy is applied to control the error arising from the linearization of the nonlinear inductionless MHD equations. The proposed method not only retains the advantages of the classical Oseen iterative scheme but also leads to a rapid rate of convergence. It is shown that the convergence rate of the new method is greatly improved under the uniqueness condition. Stability analysis and error estimates are provided. Numerical results are presented to verify the applicability and effectiveness of the new method.