On nonoverlapping domain decomposition methods for the incompressible Navier-Stokes equations
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 39 (2005) no. 6, p. 1251-1269
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 : https://doi.org/10.1051/m2an:2005046
Classification:  65F10,  65N30,  65N55
@article{M2AN_2005__39_6_1251_0,
     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 - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {39},
     number = {6},
     year = {2005},
     pages = {1251-1269},
     doi = {10.1051/m2an:2005046},
     zbl = {1085.76041},
     mrnumber = {2195911},
     language = {en},
     url = {http://http://www.numdam.org/item/M2AN_2005__39_6_1251_0}
}
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 - Modélisation Mathématique et Analyse Numérique, Tome 39 (2005) no. 6, pp. 1251-1269. doi : 10.1051/m2an:2005046. http://www.numdam.org/item/M2AN_2005__39_6_1251_0/

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