In this article, we study the stability and convergence of the Crank-Nicolson/Adams-Bashforth scheme for the two-dimensional nonstationary Navier-Stokes equations with a nonsmooth initial data. A finite element method is applied for the spatial approximation of the velocity and pressure. The time discretization is based on the implicit Crank-Nicolson scheme for the linear terms and the explicit Adams-Bashforth scheme for the nonlinear term. Moreover, we prove that the scheme is almost unconditionally stable for a nonsmooth initial data u0 with div u0 = 0, i.e., the time step τ satisfies: τ ≤ C0 if u0 ∈ H1 ∩ L∞; τ |log h| ≤ C0 if u0 ∈ H1 for the mesh size h and some positive constant C0. Finally, we obtain some error estimates for the discrete velocity and pressure under the above stability condition. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 28: 155-187, 2012
If you can't find a tool you're looking for, please click the link at the top of the page to "Go to old article view". Alternatively, view our Knowledge Base articles for additional help. Your feedback is important to us, so please let us know if you have comments or ideas for improvement.