Convergence analysis of three finite element iterative methods for the 2D/3D stationary incompressible magnetohydrodynamics

被引：106
作者：
Dong, Xiaojing [1 ]
He, Yinnian [1 ]
Zhang, Yan [1 ]
机构：
[1] Xi An Jiao Tong Univ, State Key Lab Multiphase Flow Power Engn, Sch Math & Stat, Xian 710049, Peoples R China
来源：
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING | 2014年 / 276卷
关键词：
Uniform stability; Convergence; Iterative method; Finite element method; Stationary incompressible magnetohydrodynamics; NAVIER-STOKES EQUATIONS; SPATIAL DISCRETIZATION; 2-LEVEL NEWTON; MHD EQUATIONS; APPROXIMATION; FLOWS;
D O I：
10.1016/j.cma.2014.03.022
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
Three finite element iterative methods are designed and analyzed for solving 2D/3D stationary incompressible magnetohydrodynamics (MHD). By a new technique, strong uniqueness conditions for both Stokes type iterative method (Iterative method I) and Newton iterative method (Iterative method II) are obtained, which are weaker than the ones reported in open literature. Stability and optimal convergence rates for the above two methods are derived, where the Iterative method II has an exponential convergent part with respect to iterative step m. Moreover, Oseen type iterative method (Iterative method III) is unconditionally stable and convergent under a uniqueness condition. Finally, performance of the three proposed methods is investigated by numerical experiments. (C) 2014 Elsevier B.V. All rights reserved.
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收藏
页码：287 / 311
页数：25
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