Convergence analysis of three finite element iterative methods for the 2D/3D stationary incompressible magnetohydrodynamics
Convergence analysis of three finite element iterative methods for the 2D/3D stationary incompressible magnetohydrodynamics
复制标题
2D/3D固定不可压缩磁流体动力学三种有限元迭代方法的收敛性分析
DOI：
10.1016/j.cma.2014.03.022
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发表时间：
2014-07-01
影响因子：
7.2
通讯作者：
Zhang, Yan
中科院分区：
文献类型：
--
作者：
Dong, Xiaojing;He, Yinnian;Zhang, Yan
设计并分析了求解二维/三维稳态不可压缩磁流体动力学问题的三种有限元迭代方法。通过一种新的技巧，得到了Stokes型迭代法（迭代法Ⅰ）和Newton型迭代法（迭代法Ⅱ）的强唯一性条件，该条件比公开文献中的条件弱.本文导出了这两种方法的稳定性和最优收敛速度，其中迭代法Ⅱ关于迭代步m具有指数收敛部分。此外，Oseen型迭代方法（迭代方法III）是无条件稳定的，并在唯一性条件下收敛。最后，通过数值实验研究了所提出的三种方法的性能。(C)2014爱思唯尔有限公司版权所有。
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.