Three Grad-Div stabilized Taylor-Hood finite elelments for steady Navier-Stokes eqution

Abstract:

We propose three Grad-Div stabilized Taylor-Hood finite elements for the steady Navier-Stokes equation. To keep the law of mass conservation, the Grad-Div stabilized term is added to the known discrete solutions obtained with Taylor-Hood elements, so as to get continuous velocity and pressure, and velocity solutions obeying the law of mass conservation. Under the strong uniqueness conditions, we also show that the Grad-Div stabilized Taylor-Hood finite element iterative solutions converge to the Scott-Vogelius solutions. Finally, numerical examples verify the efficiency of the finifte elements.