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On nonoverlapping domain decomposition methodsfor the incompressible Navier-Stokes equations

Published online by Cambridge University Press:  15 November 2005

Xuejun Xu ,
C. O. Chow  and
S. H. Lui
Xuejun Xu
Affiliation:
LSEC, Institute of Computational Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, PO Box 2719, Beijing, 100080, China. xxj@lsec.cc.ac.cn
C. O. Chow
Affiliation:
Institute of Mathematics, Academia Sinica, Taipei 11529, Taiwan. cchow@alum.mit.edu
S. H. Lui
Affiliation:
Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, R3T 2N2, Canada. luish@cc.umanitoba.ca
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Abstract

In this paper, a Dirichlet-Neumann substructuring domaindecomposition method is presented for a finite elementapproximation to the nonlinear Navier-Stokes equations. It isshown that the Dirichlet-Neumann domain decomposition sequenceconverges geometrically to the true solution provided the Reynoldsnumber is sufficiently small. In this method, subdomain problemsare linear. Other version where the subdomain problems are linearStokes problems is also presented.

Keywords

Nonoverlapping domain decompositionincompressible Navier-Stokes equationsfinite elementsnonlinear problems.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 39 , Issue 6 , November 2005 , pp. 1251 - 1269
Copyright
© EDP Sciences, SMAI, 2005

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