Stokes equations with penalised slip boundary conditions

Abstract

We consider the finite-element approximation of Stokes equations with slip boundary conditions imposed with the penalty method. In the case of a smooth curved boundary, our numerical results suggest that curved finite elements, regularised normal vectors or reduced integration techniques can be used to avoid a Babuska’s-type paradox and ensure the convergence of finite-element approximations to the exact solution. Convergence orders with these remedies are also compared.

Keywords:

• Stokes equations
• slip boundary conditions
• penalty method
• finite elements
• Babuska’s paradox

Acknowledgements

This research was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC).