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1. 北方工业大学理学院, 北京 100144;
2. 中国科学院数学与系统科学研究院, 北京 100190

A NON-OVERLAPPING DOMAIN DECOMPOSITION METHOD AND ITS CONVERGENCE FOR THE STOKES PROBLEM ON UNBOUNDED DOMAINS

Zheng Quan1, Wang Chongchong1, Yu Dehao2

1. College of Sciences, North China University of Technology, Beijing 100144;
2. Academy of Mathematical and System Sciences,Chinese Academy of Sciences, Beijing 100190

Abstract:

In this paper, a non-overlapping domain decomposition method by using of the FEM and the natural boundary reduction is investigated for solving the exterior boundary value problems of the Stokes equation. This method is very effective for the Stokes problem over unbounded domains especially. The D-N alternating algorithm (including continuous and discrete form) and its convergence analysis are presented, also the necessary and sufficient condition for convergence of this method is gained, then the optimal relaxation factor is obtained, finally some numerical results are illustrated.

Keywords: Unbounded domain   domain decomposition   Stokes problem   D-N alternating algorithm   convergence

DOI:

1．郑权.无界区域上基于自然边界归化的一种重叠型区域分解法及其离散化[J]. 计算数学, 1998,20(1): 11-24
2．郑权, 白荣霞, 董俊雨.各向异性外问题的Schwarz 交替法及其收敛性和误差估计[J]. 计算数学, 2009,31(1): 65-76