Stabilized Finite Element Method for Vorticity_Velocity_Pressure Formulation of the Stationary Navier-Stokes Equations

In this paper, formulated in terms of vorticity, velocity and pressure, the stationary Navier-Stokes equations are discretized by stabilized finite element methods. The method is consistent and stable for any combination of discrete vorticity, velocity and pressure spaces without requiring the B-B condition. The existence and uniqueness of the continuous and discrete solutions are proved in the case of sufficient viscosity or small data. The convergence and the optimal error rate are obtained.