Two-level method based on finite element and Crank-Nicolson extrapolation for the time-dependent Navier-Stokes equations. (English) Zbl 1130.76365
Summary: A fully discrete two-level finite element method (the two-level method) is presented for solving the two-dimensional time-dependent Navier-Stokes problem. The method requires a Crank-Nicolson extrapolation solution on a spatial-time coarse grid and a backward Euler solution on a space-time fine grid . The error estimates of optimal order of the discrete solution for the two-level method are derived. Compared with the standard Crank-Nicolson extrapolation method (the one-level method) based on a space-time fine grid , the two-level method is of the error estimates of the same order as the one-level method in the H-norm for velocity and the L-norm for pressure. However, the two-level method involves much less work than the one-level method.
|76M10||Finite element methods (fluid mechanics)|
|35Q30||Stokes and Navier-Stokes equations|
|65N30||Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)|
|76D06||Statistical solutions of Navier-Stokes and related equations|