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

Content Provider	Springer Nature Link
Author	Dong, Xiaojing Zhang, Guodong An, Yongzheng Liu, Hong
Copyright Year	2015
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 = $\tfrac{{N\|\|f\|\|_{ - 1} }} {{\nu ^2 }}$ ≤ $$\tfrac{1}{{\sqrt 2 + 1}}$$ , 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.
Ending Page	872
Page Count	10
Starting Page	863
File Format	PDF
ISSN	02534827
e-ISSN	15732754
Journal	Applied Mathematics and Mechanics
Issue Number	7
Volume Number	36
Language	English
Publisher	Shanghai University
Publisher Date	2015-06-05
Publisher Place	Shanghai
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Stokes iteration convergence Newton iteration Mechanics Applications of Mathematics Mathematical Modeling and Industrial Mathematics Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods Finite element methods Navier-Stokes equation stability Navier-Stokes equations
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Mechanics of Materials Mechanical Engineering

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