GAUGE-UZAWA METHODS FOR THE NAVIER-STOKES EQUATIONS WITH NONLINEAR SLIP BOUNDARY CONDITIONS

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. Key words. Navier-Stokes equations, nonlinear slip boundary, variational inequality, Gauge-Uzawa method, finite element approximation. 1