On the effectiveness of the approximate inertial manifold -- a computational study
We present a computational study evaluating the effectiveness of the nonlinear Galerkin method for dissipative evolution equations. We begin by reviewing the theoretical estimates of the rate of convergence for both the standard spectral Galerkin and the nonlinear Galerkin methods. We demonstrate the validity of our assertions with numerical simulations of the forced dissipative Burgers equation and of the forced Kuramoto-Sivashinsky equation. These simulations also demonstrate that the analytical upper bounds derived for the rates of convergence of both the standard Galerkin and the nonlinear Galerkin methods are nearly sharp.
scientific article; zbMATH DE number 832064
scientific article