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

Authors:
Yuan Li;Rong An
Affiliations:
College of Mathematics and Information Science, Wenzhou University, Wenzhou, PR China;College of Mathematics and Information Science, Wenzhou University, Wenzhou, PR China
Venue:
Applied Numerical Mathematics
Year:
2011

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Abstract

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.