Optimal first-order error estimates of a fully segregation scheme for   the Navier-Stokes equations
  A first-order linear fully discrete scheme is studied for the incompressible time-dependent Navier-Stokes equations in three-dimensional domains. This scheme, based on an incremental pressure projection method, decouples each component of the velocity and the pressure, solving in each time step, a linear convection-diffusion problem for each component of the velocity and a Poisson-Neumann problem for the pressure.   Using first-order \emph{inf-sup} stable $C^0$-finite elements, optimal error estimates of order $O(k+h)$ are deduced without imposing constraints on $h$ and $k$, the mesh size and the time step, respectively.   Finally, some numerical results are presented according the theoretical analysis, and also comparing to other current first-order segregated schemes. 
F. Guill\'en-Gonz\'alez and M.V. Redondo-Neble
math.NA