On the effectiveness of the approximate inertial manifold -- a computational study
type: Item
instance of: scholarly article
title: On the effectiveness of the approximate inertial manifold -- a computational study
zbMATH Open document ID: 0838.76066
DOI: 10.1007/BF00312444
author: Don A. Jones
author: L. G. Margolin
author: E. S. Titi
published in: Theoretical and Computational Fluid Dynamics
publication date: 1996-06-09T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 76M25
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 65M70
zbMATH DE Number: 832064
zbMATH Keywords: spectral Galerkin methods
zbMATH Keywords: nonlinear Galerkin method
zbMATH Keywords: dissipative evolution equations
zbMATH Keywords: convergence
zbMATH Keywords: forced dissipative Burgers equation
zbMATH Keywords: forced Kuramoto-Sivashinsky equation
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 832064