Operator splitting methods for the Navier-Stokes equations with nonlinear slip boundary conditions
Y. Li 1, K. Li 21 College of Mathematics and Information Science, Wenzhou University, Wenzhou, 325035, P.R. China.
2 School of Science, Xi'an Jiaotong University, Xi'an, 710049, P.R. China.
Received by the editors July 7, 2009 and, in revised form, April 19, 2010.
In this paper, the $theta$ scheme of operator splitting methods is applied to the Navier-Stokes equations with nonlinear slip boundary conditions whose variational formulation is the variational inequality of the second kind with the Navier-Stokes operator. Firstly, we introduce the multiplier such that the variational inequality is equivalent to the variational identity. Subsequently, we give the $theta$ scheme to compute the variational identity and consider the finite element approximation of the $theta$ scheme. The stability and convergence of the $theta$ scheme are showed. Finally, we give the numerical results.AMS subject classifications: 35Q30, 65N12
Key words: Navier-Stokes Equations, Nonlinear Slip Boundary Conditions, Operator Splitting Method, $theta$-Scheme, Finite Element Approximation.
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