Error estimates of optimal order in a fractional-step scheme for the 3D Navier-Stokes equations

Abstract

We present some improvements on the error estimates obtained by J.Blasco and R.Codina for a viscosity-splitting in time scheme, with finite element approximation, applied to the 3D Navier-Stokes equations. The key is to obtain new error estimates for the discrete in time derivative of velocity, which let us to reach, in particular, error of order one (in time and space) for the pressure approximation.