The stabilized extrapolated trapezoidal finite-element method for the Navier–Stokes equations

We consider a fully discrete stabilized finite-element method for the Navier–Stokes equations which is unconditionally stable and has second order temporal accuracy of O(k2+hk+O(k2+hk+ spatial error). The method involves a simple artificial viscosity stabilization of the linear system for the approximation of the new time level connected to anti-diffusion of its effects at the old time level, lowering the cell Reynolds number of the Oseen problem to O(1)O(1). The method requires only the solution of one linear system (arising from an Oseen problem) per time step. The effectiveness of the method is illustrated in several numerical experiments.