We consider a variational formulation of the three-dimensional Navier-Stokes equations with mixed boundary conditions and prove that the variational problem admits a solution provided that the domain satisfies a suitable regularity assumption. Next, we propose a finite element discretization relying on the Galerkin method and establish a priori and a posteriori error estimates.
Mots-clés : three-dimensional Navier-Stokes equations, mixed boundary conditions, finite element methods, a priori error estimates, a posteriori error estimates
@article{M2AN_2009__43_6_1185_0,
author = {Bernardi, Christine and Hecht, Fr\'ed\'eric and Verf\"urth, R\"udiger},
title = {A finite element discretization of the three-dimensional {Navier-Stokes} equations with mixed boundary conditions},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {1185--1201},
publisher = {EDP-Sciences},
volume = {43},
number = {6},
year = {2009},
doi = {10.1051/m2an/2009035},
mrnumber = {2588437},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/m2an/2009035/}
}
TY - JOUR AU - Bernardi, Christine AU - Hecht, Frédéric AU - Verfürth, Rüdiger TI - A finite element discretization of the three-dimensional Navier-Stokes equations with mixed boundary conditions JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2009 SP - 1185 EP - 1201 VL - 43 IS - 6 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an/2009035/ DO - 10.1051/m2an/2009035 LA - en ID - M2AN_2009__43_6_1185_0 ER -
%0 Journal Article %A Bernardi, Christine %A Hecht, Frédéric %A Verfürth, Rüdiger %T A finite element discretization of the three-dimensional Navier-Stokes equations with mixed boundary conditions %J ESAIM: Modélisation mathématique et analyse numérique %D 2009 %P 1185-1201 %V 43 %N 6 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an/2009035/ %R 10.1051/m2an/2009035 %G en %F M2AN_2009__43_6_1185_0
Bernardi, Christine; Hecht, Frédéric; Verfürth, Rüdiger. A finite element discretization of the three-dimensional Navier-Stokes equations with mixed boundary conditions. ESAIM: Modélisation mathématique et analyse numérique, Tome 43 (2009) no. 6, pp. 1185-1201. doi : 10.1051/m2an/2009035. http://archive.numdam.org/articles/10.1051/m2an/2009035/
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