Abstract: This paper proposes a new nonconforming finite difference streamline diffusion method to solve incompressible time-dependent Navier-Stokes equations with a high Reynolds number. The backwards difference in time and the Crouzeix-Raviart (CR) element combined with the P0 element in space are used. The result shows that this scheme has good stabilities and error estimates independent of the viscosity coefficient.

Key words: inverse problems, nonlinear ill-posed operator equations, Newton type method, implicit iterative method, iteration stopping rule, Navier-Stokes equation, high Reynolds number, Ladyzhenskaya-Babuˇska-Brezzi (LBB) condition, finite difference streamline diffusion method, discrete Gronwall’s inequality