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

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

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

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topXu, 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 - Modélisation Mathématique et Analyse Numérique 39.6 (2005): 1251-1269. <http://eudml.org/doc/245765>.

@article{Xu2005,

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 - Modélisation Mathématique et Analyse Numérique},

keywords = {nonoverlapping domain decomposition; incompressible Navier-Stokes equations; finite elements; nonlinear problems; convergence; Dirichlet-Neumann substructuring; finite element approximation},

language = {eng},

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/245765},

volume = {39},

year = {2005},

}

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 - Modélisation Mathématique et Analyse Numérique

PY - 2005

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/245765

ER -

## References

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