Error estimates for finite element approximations of consistent splitting schemes for incompressible flows

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 component 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.

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