Abstract
A fully discrete Crank–Nicolson leap-frog (CNLF) scheme is presented and studied for the nonstationary incompressible Navier–Stokes equations. The proposed scheme deals with the spatial discretization by Galerkin finite element method (FEM), treats the temporal discretization by CNLF method for the linear term and the semi-implicit method for nonlinear term. The almost unconditional stability, i.e., the time step is no more than a constant, is proven. By a new negative norm technique, the L2-optimal error estimates with respect to temporal and spacial orientation for the velocity are derived. At last, some numerical results are provided to justify our theoretical analysis.
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