无界区域Stokes问题非重叠型区域分解算法及其收敛性  

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

作　　者：郑权[1] 王冲冲[1] 余德浩[2] 

机构地区：[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

出　　处：《计算数学》2010年第2期113-124,共12页Mathematica Numerica Sinica

基　　金：北京市自然科学基金(1072009);国家自然科学基金(10531080);国家重点基础研究发展计划(2005CB321701)资助

摘　　要：本文研究无界区域Stokes方程外问题的利用有限元法和自然边界归化的非重叠型区域分解算法,此方法对无界区域Stokes问题非常有效.给出连续和离散情形的D-N算法及其收敛性分析,得到算法收敛的充要条件及充分条件,并得到最优的松弛因子和压缩因子,最后给出数值算例予以验证.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.

关 键 词：无界区域 区域分解 STOKES问题 D—N交替法 收敛性 

分 类 号：O241.82[理学—计算数学]