Stabilized finite element method based on the Crank-Nicolson extrapolation scheme for the time-dependent Navier-Stokes equations

This paper provides an error analysis for the Crank–Nicolson extrapolation scheme of time discretization applied to the spatially discrete stabilized finite element approximation of the two-dimensional time-dependent Navier–Stokes problem, where the finite element space pair (Xh,Mh) for the approximation (uh, p n h) of the velocity u and the pressure p is constructed by the low-order finite element: the Q1 −P0 quadrilateral element or the P1 −P0 triangle element with mesh size h. Error estimates of the numerical solution (uh , p n h) to the exact solution (u(tn), p(tn)) with tn ∈ (0, T ] are derived.