Two-Level Penalty Finite Element Methods for Navier-Stokes Equations with Nonlinear Slip Boundary Conditions
Year: 2014
International Journal of Numerical Analysis and Modeling, Vol. 11 (2014), Iss. 3 : pp. 608–623
Abstract
The two-level penalty 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. The basic idea is to solve the Navier-Stokes type variational inequality problem on a coarse mesh with mesh size $H$ in combining with solving a Stokes type variational inequality problem for simple iteration or solving a Oseen type variational inequality problem for Oseen iteration on a fine mesh with mesh size $h$. The error estimate obtained in this paper shows that if $H = O(h^{5/9})$, then the two-level penalty methods have the same convergence orders as the usual one-level penalty finite element method, which is only solving a large Navier-Stokes type variational inequality problem on the fine mesh. Hence, our methods can save an amount of computational work.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2014-IJNAM-544
International Journal of Numerical Analysis and Modeling, Vol. 11 (2014), Iss. 3 : pp. 608–623
Published online: 2014-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Navier-Stokes Equations Nonlinear Slip Boundary Conditions Variational Inequality Problem Penalty Finite Element Method Two-Level Methods.