Un résultat de convergence d'ordre deuxen temps pour l'approximation des équationsde Navier–Stokes par une technique de projectionincrémentale

Abstract

The Navier–Stokes equations are approximated by means ofa fractional step, Chorin–Temam projection method; the time derivativeis approximated by a three-level backward finite difference, whereasthe approximation in space is performed by a Galerkin technique.It is shown that the proposed scheme yields an errorof ${\cal O}(\delta t^2 + h^{l+1})$ for the velocity in the norm of l ²(L²(Ω)^d), where l ≥ 1 isthe polynomial degree of the velocity approximation. It is also shownthat the splitting error of projection schemes based on theincremental pressure correction is of ${\cal O}(\delta t^2)$ independent of theapproximation order of the velocity time derivative.