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Penalty finite element method for Navier–Stokes equations with nonlinear slip boundary conditions
Author(s) -
Li Yuan,
An Rong
Publication year - 2011
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.2574
Subject(s) - finite element method , mathematics , penalty method , slip (aerodynamics) , boundary value problem , nonlinear system , mathematical analysis , extended finite element method , variational inequality , mixed finite element method , boundary knot method , navier–stokes equations , boundary element method , mathematical optimization , physics , mechanics , compressibility , quantum mechanics , thermodynamics
SUMMARY The penalty finite element method for Navier–Stokes 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 © 2011 John Wiley & Sons, Ltd.