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Finite element approximation of incompressible Navier-Stokes equations with slip boundary condition. (English) Zbl 0596.76031

We consider a mixed finite element approximation of the stationary, incompressible Navier-Stokes equations with slip boundary conditions, which plays an important rôle in the simulation of flows with free angles of attack and high Reynold’s numbers.
The central point is a saddle point formulation of the boundary conditions which avoids the well-known Babuška paradox when approximating smooth domains by polyhedrons. We prove that for the new formulation one can use any stable mixed finite element for the Navier- Stokes equations with no-slip boundary conditions provided suitable bubble functions on the boundary are added to the velocity space.
We obtain optimal error estimates under minimal regularity assumptions for the solution of the continuous problem. The techniques apply as well to the more general Navier boundary conditions.

MSC:

76D05 Navier-Stokes equations for incompressible viscous fluids
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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References:

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