A finite element discretization of the three-dimensional Navier-Stokes equations with mixed boundary conditions
Bernardi, Christine ; Hecht, Frédéric ; Verfürth, Rüdiger1
1 Ruhr-Universität Bochum, Fakultät für Mathematik, 44780 Bochum, Germany.
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 43 (2009) no. 6, pp. 1185-1201.

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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 : 10.1051/m2an/2009035
Classification : 65N30, 65N15, 65J15
Mots-clés : three-dimensional Navier-Stokes equations, mixed boundary conditions, finite element methods, a priori error estimates, a posteriori error estimates

Bernardi, Christine  ; Hecht, Frédéric  ; Verfürth, Rüdiger 1

1 Ruhr-Universität Bochum, Fakultät für Mathematik, 44780 Bochum, Germany. 
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     title = {A finite element discretization of the three-dimensional {Navier-Stokes} equations with mixed boundary conditions},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {1185--1201},
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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 , Tome 43 (2009) no. 6, pp. 1185-1201. doi : 10.1051/m2an/2009035. https://geodesic-test.mathdoc.fr/articles/10.1051/m2an/2009035/

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