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.
@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: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {43},
year = {2009},
pages = {1185-1201},
doi = {10.1051/m2an/2009035},
mrnumber = {2588437},
zbl = {pre05636851},
language = {en},
url = {http://dml.mathdoc.fr/item/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: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 43 (2009) pp. 1185-1201. doi : 10.1051/m2an/2009035. http://gdmltest.u-ga.fr/item/M2AN_2009__43_6_1185_0/
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