A finite element discretization of the three-dimensional Navier–Stokes equations with mixed boundary conditions
Christine Bernardi, Frédéric Hecht, Rüdiger Verfürth (2009)
ESAIM: Mathematical Modelling and Numerical Analysis
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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 and error estimates.