Two-level pressure projection finite element methods for Navier-Stokes equations with nonlinear slip boundary conditions

• Autores: Yuan Li, An Rong
• Localización: Applied numerical mathematics, ISSN-e 0168-9274, Vol. 61, Nº. 3, 2011, págs. 285-297
• Idioma: inglés
• DOI: 10.1016/j.apnum.2010.10.005
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• Resumen

  • 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 P1�P1 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(H2), 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.