# 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

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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 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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