WITHDRAWN: Two-grid Arrow-Hurwicz iterative finite element methods for the stationary magnetohydrodynamics flow

Abstract

In this paper, we propose and analyze three kinds of two-grid Arrow-Hurwicz (A-H) iterative finite element methodsfor the stationary incompressible magnetohydrodynamics (MHD) equations, which adopt the existingA-H iterative method to obtain the coarse mesh solution, and then correct the solution by threedifferent one-step schemes (Oseen type, Stokes type and Newton type) on the fine mesh. These methods combine the A-H iterative method and the two-grid strategy, maintaining the advantage of both methods and overcoming some of their limitations. Rigorous analysis of the optimal error estimate and stability for three methods are provided. Ample numerical experiments are reported to validate the theoretical results and the efficiency of the numerical schemes.Mathematics Subject Classification (2000) 65N15 · 65N30 · 65N12 · 65M12