Volume 5, Issue 1
Gauge-Uzawa Methods for the Navier-Stokes Equations with Nonlinear Slip Boundary Conditions

Hailong Qiu ,  Liquan Mei and Zhangxin Chen

Int. J. Numer. Anal. Mod. B, 5 (2014), pp. 46-56

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  • Abstract

In this paper, the Gauge-Uzawa method is applied to solve the Navier-Stokes equations with nonlinear slip boundary conditions whose variational formulation is a variational inequality of the second kind with the Navier-Stokes operator. In [1], a multiplier was introduced such that the variational inequality is equivalent to the variational identity. We give the Gauge-Uzawa scheme to compute this variational identity and provide a finite element approximation for the Gauge-Uzawa scheme. The stability of the Gauge-Uzawa scheme is showed. Finally, numerical experiments are given, which confirm the theoretical analysis and demonstrate the efficiency of the new method.

  • History

Published online: 2014-05

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