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.
Keywords: nonoverlapping domain decomposition, incompressible Navier-Stokes equations, finite elements, nonlinear problems
@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: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {1251--1269},
year = {2005},
publisher = {EDP Sciences},
volume = {39},
number = {6},
doi = {10.1051/m2an:2005046},
mrnumber = {2195911},
zbl = {1085.76041},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an:2005046/}
}
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: Modélisation mathématique et analyse numérique PY - 2005 SP - 1251 EP - 1269 VL - 39 IS - 6 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/m2an:2005046/ DO - 10.1051/m2an:2005046 LA - en ID - M2AN_2005__39_6_1251_0 ER -
%0 Journal Article %A Xu, Xuejun %A Chow, C. O. %A Lui, S. H. %T On nonoverlapping domain decomposition methods for the incompressible Navier-Stokes equations %J ESAIM: Modélisation mathématique et analyse numérique %D 2005 %P 1251-1269 %V 39 %N 6 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/m2an:2005046/ %R 10.1051/m2an:2005046 %G en %F 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: Modélisation mathématique et analyse numérique, Tome 39 (2005) no. 6, pp. 1251-1269. doi: 10.1051/m2an:2005046
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