A New Higher Order Fractional-Step Method for the Incompressible Navier-Stokes Equations

Abstract

In this paper, we present a rigorous error analysis of a new higher order fractional-step scheme for approximation of the time-dependent Navier-Stokes equations. The main feature of the proposed scheme is twofold. First, it is a two-step scheme in which the incompressibility and nonlinearities are split. Second, this scheme is a linear scheme and is simple to implement. It is shown that the proposed scheme possesses the convergence rate $\mathcal O((\Delta t)^{3/2})$ in the discrete $l^2$(H$_0^1)\cap$ $l^\infty$(L$^2$)-norm for the end-of-step velocity. Two different numerical experiments are presented to confirm the theoretical analysis and the efficiency of the proposed scheme.