New conditions of stability and convergence of Stokes and Newton iterations for Navier-Stokes equations

作     者：Guodong ZHANG Xiaojing DONG Yongzheng AN Hong LIU 

作者机构：School of Mathematics and StatisticsXi'an Jiaotong University 

出 版 物：《Applied Mathematics and Mechanics(English Edition)》 (应用数学和力学（英文版）)

年 卷 期：2015年第36卷第7期

页      面：863-872页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by the National Natural Science Foundation of China(No.11271298) 

主　　题：Navier-Stokes equation Stokes iteration Newton iteration stability,convergence 

摘      要：This paper considers Stokes and Newton iterations to solve stationary Navier- Stokes equations based on the finite element discretization. We obtain new sufficient conditions of stability and convergence for the two iterations. Specifically, when 0 〈 σ =N｜｜f｜｜-1/v2≤1/√2＋1 , the Stokes iteration is stable and convergent, where N is defined in the paper. When 0 〈 σ ≤5/11, the Newton iteration is stable and convergent. This work gives a more accurate admissible range of data for stability and convergence of the two schemes, which improves the previous results. A numerical test is given to verify the theory.