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On nonoverlapping domain decomposition methods for 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 domain decomposition method is presented for a finite element approximation to the nonlinear Navier-Stokes equations. It is shown that the Dirichlet-Neumann domain decomposition sequence converges geometrically to the true solution provided the Reynolds number is sufficiently small. In this method, subdomain problems are linear. Other version where the subdomain problems are linear Stokes 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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