On the computation of inertial manifolds

C. Foias; M. S. Jolly; I. G. Kevrekidis; G. R. Sell; E. S. Titi

doi:10.1016/0375-9601(88)90295-2

On the computation of inertial manifolds

C. Foias, M. S. Jolly, I. G. Kevrekidis, G. R. Sell, E. S. Titi

Chemical & Biological Engineering

Research output: Contribution to journal › Article › peer-review

189 Scopus citations

Abstract

A modified Galerkin (the "Euler-Galerkin") algorithmj for the computational of inertial manifolds is described and applied to reaction diffusion and the Kuramoto-Sivashinsky (KS) equation. In the context of the (KS) equation, a low-dimensional Euler-Galerkin approximation (n = 3) is distinctly superior to the traditional Galerkin of the same dimension, and comparable to a traditional Galerkin of a much higher dimension (n = 16).

Original language	English (US)
Pages (from-to)	433-436
Number of pages	4
Journal	Physics Letters A
Volume	131
Issue number	7-8
DOIs	https://doi.org/10.1016/0375-9601(88)90295-2
State	Published - Sep 5 1988

All Science Journal Classification (ASJC) codes

Physics and Astronomy(all)

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abstract = "A modified Galerkin (the {"}Euler-Galerkin{"}) algorithmj for the computational of inertial manifolds is described and applied to reaction diffusion and the Kuramoto-Sivashinsky (KS) equation. In the context of the (KS) equation, a low-dimensional Euler-Galerkin approximation (n = 3) is distinctly superior to the traditional Galerkin of the same dimension, and comparable to a traditional Galerkin of a much higher dimension (n = 16).",

author = "C. Foias and Jolly, {M. S.} and Kevrekidis, {I. G.} and Sell, {G. R.} and Titi, {E. S.}",

note = "Funding Information: An inertial manifold is a finite-dimensional, exponentially attracting, positively invariant Lipschitz This work was partially supported by NSF grants CBT-8707090, EET-8717787, DMS-8507784, and DMS-8501933, DOE grant DE-FG02-86ER25020, and the Applied and Computational Mathematics Pmgram/DARPA.",

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T1 - On the computation of inertial manifolds

AU - Foias, C.

AU - Jolly, M. S.

AU - Kevrekidis, I. G.

AU - Sell, G. R.

AU - Titi, E. S.

N1 - Funding Information: An inertial manifold is a finite-dimensional, exponentially attracting, positively invariant Lipschitz This work was partially supported by NSF grants CBT-8707090, EET-8717787, DMS-8507784, and DMS-8501933, DOE grant DE-FG02-86ER25020, and the Applied and Computational Mathematics Pmgram/DARPA.

PY - 1988/9/5

Y1 - 1988/9/5

N2 - A modified Galerkin (the "Euler-Galerkin") algorithmj for the computational of inertial manifolds is described and applied to reaction diffusion and the Kuramoto-Sivashinsky (KS) equation. In the context of the (KS) equation, a low-dimensional Euler-Galerkin approximation (n = 3) is distinctly superior to the traditional Galerkin of the same dimension, and comparable to a traditional Galerkin of a much higher dimension (n = 16).

AB - A modified Galerkin (the "Euler-Galerkin") algorithmj for the computational of inertial manifolds is described and applied to reaction diffusion and the Kuramoto-Sivashinsky (KS) equation. In the context of the (KS) equation, a low-dimensional Euler-Galerkin approximation (n = 3) is distinctly superior to the traditional Galerkin of the same dimension, and comparable to a traditional Galerkin of a much higher dimension (n = 16).

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On the computation of inertial manifolds

Abstract

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