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three-dimensional navier–stokes equations

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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A finite element discretization of the three-dimensional Navier–Stokes equations with mixed boundary conditions
Christine Bernardi, Frédéric Hecht, Rüdiger Verfürth
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 43 / Issue 6 / November 2009

Published online by Cambridge University Press:

21 August 2009, pp. 1185-1201

Print publication:

November 2009
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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.