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Int. J. Numer. Anal. Mod., 7 (2010), pp. 785-805. |
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Operator splitting methods for the Navier-Stokes equations with nonlinear slip boundary conditions Y. Li 1, K. Li 2 1 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. Abstract
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, 65N12Key words: Navier-Stokes Equations, Nonlinear Slip Boundary Conditions, Operator Splitting Method, $theta$-Scheme, Finite Element Approximation. Email: yuanli1984@yahoo.com.cn, ktli@mail.xjtu.edu.cn |