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 (X_h, M_h) for the approximation (u_h ⁿ, p_h ⁿ ) of the velocity u and the pressure p is constructed by the low-order finite element: the Q₁ ? P₀ quadrilateral element or the P ₁ ? P₀ triangle element with mesh size h. Error estimates of the numerical solution (u_h ⁿ, p_h ⁿ) to the exact solution (u(t_n), p(t_n)) with t_n ∈ (0, T] are derived. © 2006 American Mathematical Society.