A postprocessed Galerkin method with Chebyshev or Legendre polynomials

We present an approximate-inertial-manifold-based postprocess to enhance Ch ebyshev or Legendre spectral Galerkin methods. We prove that the postproces s improves the order of convergence of the Galerkin solution, yielding the same accuracy as the nonlinear Galerkin method. Numerical experiments show that the new method is computationally more efficient than Galerkin and non linear Galerkin methods. New approximation results for Chebyshev polynomial s are presented. Mathematics Subject Classification (1991): 65M60.