On nonoverlapping domain decomposition methods for the incompressible Navier-Stokes equations

Xuejun Xu; C. O. Chow; S. H. Lui

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 39, Issue: 6, page 1251-1269
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Xu, Xuejun, Chow, C. O., and Lui, S. H.. "On nonoverlapping domain decomposition methods for the incompressible Navier-Stokes equations." ESAIM: Mathematical Modelling and Numerical Analysis 39.6 (2010): 1251-1269. <http://eudml.org/doc/194303>.

@article{Xu2010,
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. },
author = {Xu, Xuejun, Chow, C. O., Lui, S. H.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Nonoverlapping domain decomposition; incompressible Navier-Stokes equations; finite elements; nonlinear problems.; convergence; Dirichlet-Neumann substructuring; finite element approximation},
language = {eng},
month = {3},
number = {6},
pages = {1251-1269},
publisher = {EDP Sciences},
title = {On nonoverlapping domain decomposition methods for the incompressible Navier-Stokes equations},
url = {http://eudml.org/doc/194303},
volume = {39},
year = {2010},
}

TY - JOUR
AU - Xu, Xuejun
AU - Chow, C. O.
AU - Lui, S. H.
TI - On nonoverlapping domain decomposition methods for the incompressible Navier-Stokes equations
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 39
IS - 6
SP - 1251
EP - 1269
AB - 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.
LA - eng
KW - Nonoverlapping domain decomposition; incompressible Navier-Stokes equations; finite elements; nonlinear problems.; convergence; Dirichlet-Neumann substructuring; finite element approximation
UR - http://eudml.org/doc/194303
ER -

References

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