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On the Geometric Convergence of the Uzawa Algorithm for Steady Incompressible NavierStokes Equations(PDF)

《南京师范大学学报》(自然科学版)[ISSN:1001-4616/CN:32-1239/N]

Issue:
2014年02期
Page:
15-
Research Field:
数学
Publishing date:

Info

Title:
On the Geometric Convergence of the Uzawa Algorithm for Steady Incompressible NavierStokes Equations
Author(s):
Chen PuyinHuang Jianguo
Department of Mathematics,Shanghai Jiao Tong University,Shanghai 200240,China
Keywords:
NavierStokes equationsUzawa methodcnvergence rate analysis
PACS:
O24
DOI:
-
Abstract:
Temam proposed an Uzawa algorithm for solving steady incompressible NavierStokes equations and proved its convergence.However,the convergence rate analysis remains open until now.We prove in this paper that this method converges geometrically.

References:

[1]Adams R A.Sobolev Spaces[M].New York:Academic Press,1975.
[2]Temam R.NavierStokes Equations[M].North Holland:Amsterdam,1984.
[3]Girault V,Raviart P A.Finite Element Approximations of the NavierStokes Equations[M].New York:Springer,1986.
[4]Quarteroni A,Valli A.Numerical Approximation of Partial Differential Equations[M].Berlin:Springer,1994.
[5]Nochetto R H,Pyo J H.Optimal relaxation parameter for the Uzawa method[J].Numer Math,2004,98:695-702.

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Last Update: 2014-06-30