Convergence of fourier methods for Navier-Stokes equations

The Fourier-Galerkin method is used to simulate fluid flows in two and three dimensions, on domains with periodic boundary conditions. It is proved that the numerical solution converges towards the solution of Navier-Stokes equations. The rate of convergence depends on the smoothness of the mathematical solution. Finally, it is shown that the Fourier-Galerkin method can be interpreted as a projection method. This observation may lead to more sophisticated convergence proofs.