Result of convergence of order two in time for approximation of Navier-Stokes equations by means of an incremental projection method

The Navier-Stokes equations are approximated by means of a fractional step, Chorin-Temam projection method; the time derivative is approximated by a t hree-level backward finite difference, whereas the approximation in space i s performed by a Galerkin technique. It is shown that the proposed scheme y ields an error of O(delta t(2) + h(l+1)) for the velocity in the norm of l( 2)(L-2(Omega)(d)), where l greater than or equal to 1 is the polynomial deg ree of the velocity approximation. It is also shown that the splitting erro r of projection schemes based on the incremental pressure correction is of O(delta t(2)) independent of the approximation order of the velocity time d erivative.