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Finite element approximation on incompressible Navier-Stokes equations with slip boundary condition

  • On the Numerical Solution of the First Biharmonic Boundary Value Problem
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Summary

We consider a mixed finite element approximation of the stationary, incompressible Navier-Stokes equations with slip boundary condition, which plays an important rôle in the simulation of flows with free surfaces and incompressible viscous flows at high 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 condition 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 continous problem. The techniques apply as well to the more general Navier boundary condition.

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  1. Institut für Angewandte Mathematik, Universität Heidelberg, Im Neuenheimer Feld 293, D-6900, Heidelberg, Federal Republic of Germany

    Rüdiger Verfürth

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  1. Rüdiger Verfürth
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Verfürth, R. Finite element approximation on incompressible Navier-Stokes equations with slip boundary condition. Numer. Math. 50, 697–721 (1986). https://doi.org/10.1007/BF01398380

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  • DOI: https://doi.org/10.1007/BF01398380

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