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, Volume 43 (2009) no. 6, p. 1185-1201

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.

DOI : https://doi.org/10.1051/m2an/2009035
Classification:  65N30,  65N15,  65J15
Keywords: 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: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {43},
     number = {6},
     year = {2009},
     pages = {1185-1201},
     doi = {10.1051/m2an/2009035},
     zbl = {pre05636851},
     mrnumber = {2588437},
     language = {en},
     url = {http://www.numdam.org/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, Volume 43 (2009) no. 6, pp. 1185-1201. doi : 10.1051/m2an/2009035. http://www.numdam.org/item/M2AN_2009__43_6_1185_0/

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