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

doi:10.1007/s10483-015-1953-9

Abstract

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

2010 MSC Number:

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

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