Abstract
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.
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The authors thank the two referees for their constructive remarks and comments.
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Communicated by: Jon Wilkening
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Djoko, J.K., Koko, J. & Konlack, S. Stokes equations under Tresca friction boundary condition: a truncated approach. Adv Comput Math 48, 22 (2022). https://doi.org/10.1007/s10444-022-09933-7
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DOI: https://doi.org/10.1007/s10444-022-09933-7
Keywords
- Stokes equations
- Tresca friction law
- Cutoff function
- Error estimates
- Finite element approximation
- Linear convergence
- Numerical simulations