Fourier spectral projection method and nonlinear convergence analysis for Navier–Stokes equations

Abstract

In this paper, we investigate the convergence rate of the Fourier spectral projection methods for the periodic problem of n-dimensional Navier–Stokes equations. Based on some alternative formulations of the Navier–Stokes equations and the related projection methods, the error estimates are carried out by a global nonlinear error analysis. It simplifies the analysis, relaxes the restriction on the time step size, weakens the regularity requirements on the genuine solution, and leads to some improved convergence results. A new correction technique is proposed for improving the accuracy of the numerical pressure.