Error correction iterative method for the stationary incompressible MHD flow

Abstract

A new iterative finite element method for solving the stationary incompressible magnetohydrodynamics (MHD) equations is derived in this paper. The method consists of two steps at each iteration step, we need first to solve the MHD equations by the Oseen‐type iterative scheme, and then an error correction strategy is applied to control the error arising from the linearization of the nonlinear MHD equations. The new method not only maintains the advantage of the standard Oseen‐type scheme but also possesses a rapid rate of convergence. It is proved that the convergence rate of the proposed method is increased greatly under the uniqueness condition. The uniform stability and convergence of the new scheme are analyzed. Ample numerical experiments are performed to validate the accuracy and the efficiency of the new numerical scheme.

WITHDRAWN: Two-grid Arrow-Hurwicz iterative finite element methods for the stationary magnetohydrodynamics flow

“…Combining above two inequalities with (38), (39) and Theorem 1, we get the desired estimate and complete the proof.…”

“…A two-level Newton iteration method was studied and analyzed by Dong and He [8]. A error correction iterative was given out in [39]. The other efficient iterative methods can be seen in [9,10].…”