Abstract. We study a finite element approximation for the consistent
splitting scheme proposed in [11] for the time dependent Navier-Stokes
equations.  At each time step, we only need to solve a Poisson type
equation for each com- ponent of the velocity and the pressure. We
cast the finite element approximation in an abstract form using
appropriately defined discrete differential operators, and derive
optimal error estimates for both velocity and pressure under the
inf-sup assumption.