Stokes equations under Tresca friction boundary condition: a truncated approach
Résumé
A priori error analysis of the finite element approximation of Stokes equations under slip boundary condition of friction type has been centered on the interpolation error on the slip zone. In this work, we propose a novel approach based on the approximation of the tangential component of traction force by a truncated (cutoff) function. More precisely, we carry out (i) a complete analysis of the truncated formulation from the continuous to discrete level in two and three dimensions. In particular, we show linear convergence rate of the finite element solution by assuming standard regularity of the weak solution. This improves all previous results. (ii) The description of our solution strategy, (iii) a verification of the convergence properties with analytic solution and benchmark tests.
Mots clés
- Finite element approximation
- finite element approximation
- error estimates
- cut off function
- Nitsche method
- variational inequality
- Numerical simulations
- Linear convergence
- Cutoff function
- Tresca friction law
- Stokes equations
- Rate of convergence
- Error estimates
- DG approximations
- Anisotropic slip boundary condition
- Power law
Domaines
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