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 

机构地区：[1]School of Mathematics and Statistics,Xi'an Jiaotong University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2015年第7期863-872,共10页应用数学和力学（英文版）

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

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.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.

关 键 词：Navier-Stokes equation Stokes iteration Newton iteration stability convergence 

分 类 号：O175[理学—数学]