Journal
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS
Volume 69, Issue 3, Pages 550-566Publisher
WILEY-BLACKWELL
DOI: 10.1002/fld.2574
Keywords
Navier-Stokes equations; nonlinear slip boundary conditions; variational inequality problem; penalty finite element approximation; error estimate
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Funding
- National Natural Science Foundation of China [10901122, 11001205]
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The penalty finite element method for NavierStokes equations with nonlinear slip boundary conditions is investigated in this paper. Since this class of nonlinear slip boundary conditions include the subdifferential property, the weak variational formulation is a variational inequality problem of the second kind. Using the penalty finite element approximation, we obtain optimal error estimates between the exact solution and the finite element approximation solution. Finally, we show the numerical results which are in full agreement with the theoretical results. Copyright (C) 2011 John Wiley & Sons, Ltd.
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