An enhanced pseudospectral Chebyshev method for dissipative partial differential equations
type: Item
instance of: scholarly article
title: An enhanced pseudospectral Chebyshev method for dissipative partial differential equations
zbMATH Open document ID: 0944.65108
DOI: 10.1016/S0377-0427(99)00173-9
author: Javier de Frutos
author: Julia Novo
published in: Journal of Computational and Applied Mathematics
publication date: 2000-09-26T00:00:00Z
review text: Inertial manifolds were introduced by R. Temam and co-workers in 1985 [cf. \textit{R. Temam}, Infinite-dimensional dynamical systems in mechanics and physics (1988; Zbl 0662.35001)] for the study of nonlinear dissipative partial differential equations from a dynamical systems points of view. For the numerical solution of such problems, approximate inertial manifolds (AIM) were also considered. As it was analyzed by \textit{B. Garcia-Archilla}, \textit{J. Novo} and \textit{E. Titi} [SIAM J. Numer. Anal. 35, No. 3, 941-972 (1998; Zbl 0914.65105)] for a spectral Galerkin method using eigenfunctions, it is sufficient to evaluate the AIM only once after the time integration. With the paper in hand, the authors extend this idea of postprocessing to more realistic methods using orthogonal Chebyshev polynomials instead of unknown eigenfunctions. In addition, this new method is shown to be convergent and efficient even for limited regularity of the exact solution. Numerical examples for the viscous Burgers equation illustrate the method. For the time integration, a variable stepsize variable order backward differentiation formula is used.
Mathematics Subject Classification ID: 65M70
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35Q53
zbMATH DE Number: 1423314
zbMATH Keywords: pseudospectral Chebyshev method
zbMATH Keywords: dissipative partial differential equations
zbMATH Keywords: convergence
zbMATH Keywords: numerical examples
zbMATH Keywords: approximate inertial manifolds
zbMATH Keywords: spectral Galerkin method
zbMATH Keywords: viscous Burgers equation
zbMATH Keywords: variable stepsize
zbMATH Keywords: backward differentiation formula
MaRDI profile type: Publication
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full work available at URL: s0377-0427(99)00173-9
OpenAlex ID: W2150322192
description: scientific article; zbMATH DE number 1423314