Geodesic
On nonoverlapping domain decomposition methods for the incompressible Navier-Stokes equations
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 39 (2005) no. 6, pp. 1251-1269

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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.

DOI : 10.1051/m2an:2005046
Classification : 65F10, 65N30, 65N55
Keywords: nonoverlapping domain decomposition, incompressible Navier-Stokes equations, finite elements, nonlinear problems 
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     author = {Xu, Xuejun and Chow, C. O. and Lui, S. H.},
     title = {On nonoverlapping domain decomposition methods for the incompressible {Navier-Stokes} equations},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {1251--1269},
     publisher = {EDP-Sciences},
     volume = {39},
     number = {6},
     year = {2005},
     doi = {10.1051/m2an:2005046},
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     zbl = {1085.76041},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an:2005046/}
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Xu, Xuejun; Chow, C. O.; Lui, S. H. On nonoverlapping domain decomposition methods for the incompressible Navier-Stokes equations. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 39 (2005) no. 6, pp. 1251-1269. doi: 10.1051/m2an:2005046

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