期刊
APPLIED NUMERICAL MATHEMATICS
卷 61, 期 3, 页码 285-297出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.apnum.2010.10.005
关键词
Navier-Stokes equations; Nonlinear slip boundary conditions; Variational inequality problem; Stabilized finite element; Two-level methods
资金
- National Natural Science Foundation of China [10901122, 11001205]
The two-level pressure projection stabilized finite element methods for Navier-Stokes equations with nonlinear slip boundary conditions are investigated in this paper, whose variational formulation is the Navier-Stokes type variational inequality problem of the second kind. Based on the P(1)-P(1) triangular element and using the pressure projection stabilized finite element method, we solve a small Navier-Stokes type variational inequality problem on the coarse mesh with mesh size H and solve a large Stokes type variational inequality problem for simple iteration or a large Oseen type variational inequality problem for Oseen iteration on the fine mesh with mesh size h. The error analysis obtained in this paper shows that if h = O(H(2)), the two-level stabilized methods have the same convergence orders as the usual one-level stabilized finite element methods, which is only solving a large Navier-Stokes type variational inequality problem on the fine mesh. Finally, numerical results are given to verify the theoretical analysis. (C) 2010 IMACS. Published by Elsevier B.V. All rights reserved.
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