Quasi-Optimal Error Estimates for the Incompressible Navier-Stokes   Problem Discretized by Finite Element Methods and Pressure-Correction   Projection with Velocity Stabilization
  We consider error estimates for the fully discretized instationary Navier-Stokes problem. For the spatial approximation we use conforming inf-sup stable finite element methods in conjunction with grad-div and local projection stabilization acting on the streamline derivative. For the temporal discretization a pressure-correction projection algorithm based on BDF2 is used. We can show quasi-optimal rates of convergence with respect to time and spatial discretization for all considered error measures. Some of the error estimates are quasi-robust with respect to the Reynolds number. 
Daniel Arndt, Helene Dallmann, Gert Lube
math.NA