Second order time–space iterative method for the stationary Navier–Stokes equations

A second order time–space implicit/explicit iterative scheme for the stationary Navier–Stokes equations is designed, where the spatial discretization is based on the mixed finite element method and the time discretization is based on the second order implicit/explicit (the Crank–Nicolson/Admas–Bashforth) scheme. Under a weak uniqueness condition, the optimal H1H1-L2L2 error estimates related to the mesh size hh and time step size ττ of the iterative solution (uhn,phn) to the exact solution (ũ,p̃) and the optimal L2L2 error estimate related to hh and ττ of the iterative solution uhn to the exact solution ũ are provided. In numerical aspect, some comparisons with the first order time–space iterative method are made to confirm the efficiency of the proposed second order scheme.