A New Stabilized Finite Element Method for Solving Transient Navier-Stokes Equations with High Reynolds Number (Journal of Computational Mathematics, 2020)
In this paper, we present a new stabilized finite element method for transient Navier-Stokes equations with high Reynolds number based on the projection of the velocity andpressure. We use Taylor-Hood elements and the equal order elements in space and secondorder difference in time to get the fully discrete scheme. The scheme is proven to possess theabsolute stability and the optimal error estimates. Numerical experiments show that ourmethod is effective for transient Navier-Stokes equations with high Reynolds number andthe results are in good agreement with the value of subgrid-scale eddy viscosity methods,Petro-Galerkin finite element method and streamline diffusion method.