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 ( k 2 + 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 ) . 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.