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

doi:10.1007/s10483-015-1953-9

Applied Mathematics and Mechanics (English Edition) ›› 2015, Vol. 36 ›› Issue (7): 863-872.doi: https://doi.org/10.1007/s10483-015-1953-9

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

Guodong ZHANG, Xiaojing DONG, Yongzheng AN, Hong LIU

School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, China

收稿日期:2014-05-13 修回日期:2014-09-05 出版日期:2015-07-01 发布日期:2015-07-01
通讯作者: Guodong ZHANG E-mail:zhangguodong11@stu.xjtu.edu.cn

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

Guodong ZHANG, Xiaojing DONG, Yongzheng AN, Hong LIU

School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, China

Received:2014-05-13 Revised:2014-09-05 Online:2015-07-01 Published:2015-07-01
Contact: Guodong ZHANG E-mail:zhangguodong11@stu.xjtu.edu.cn

摘要/Abstract

关键词: Navier-Stokes equation, Stokes iteration, convergence, Newton iteration, stability

Abstract: 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/($\sqrt{2}$+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.

Key words: Newton iteration, convergence, stability, Stokes iteration, Navier-Stokes equation

中图分类号:

Guodong ZHANG, Xiaojing DONG, Yongzheng AN, Hong LIU. New conditions of stability and convergence of Stokes and Newton iterations for Navier-Stokes equations[J]. Applied Mathematics and Mechanics (English Edition), 2015, 36(7): 863-872.

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

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

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