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The Navier-Stokes équations are approximated by means of a fractional step, Chorin- Temam projection method; the time derivative is approximated by a three-level backward finite dif- férence, whereas the approximation in space is performed by a Galerkin technique. It is shown that the proposed scheme yields an error of O(Ôt2 + hl+1) for the velocity in the norm of Z2(L2(^)d), where / > 1 is the polynomial degree of the velocity approximation. It is also shown that the splitting error of projection schemes based on the incrémental pressure correction is of ö(6t2) independent of the approximation order of the velocity time derivative.

Un résultat de convergence d'ordre deux en temps pour l'approximation des équations de Navier–Stokes par une technique de projection incrémentale