ON THE LARGE TIME GALERKIN APPROXIMATION OF THE NAVIER-STOKES EQUATIONS.

Peter Constantin; C. Foias; R. Temam

doi:10.1137/0721043

ON THE LARGE TIME GALERKIN APPROXIMATION OF THE NAVIER-STOKES EQUATIONS.

Peter Constantin, C. Foias, R. Temam

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35 Scopus citations

Abstract

The difficult problem of relating the large time behavior of the Navier-Stokes equations to the large time behavior of their Galerkin approximation is considered. Attention is restricted to the simplest situation dealing with stationary solutions and the question is the following one: if the computed approximation of the time dependent equations 'seems to converge' to some limit as approached t yields cent , is the same true for the exact problem and are the limits related? Some sufficient conditions (reasonably easy to verify) which guarantee a positive answer to this question are given.

Original language	English (US)
Pages (from-to)	615-634
Number of pages	20
Journal	SIAM Journal on Numerical Analysis
Volume	21
Issue number	4
DOIs	https://doi.org/10.1137/0721043
State	Published - 1984

All Science Journal Classification (ASJC) codes

Computational Mathematics
Applied Mathematics
Numerical Analysis

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title = "ON THE LARGE TIME GALERKIN APPROXIMATION OF THE NAVIER-STOKES EQUATIONS.",

abstract = "The difficult problem of relating the large time behavior of the Navier-Stokes equations to the large time behavior of their Galerkin approximation is considered. Attention is restricted to the simplest situation dealing with stationary solutions and the question is the following one: if the computed approximation of the time dependent equations 'seems to converge' to some limit as approached t yields cent , is the same true for the exact problem and are the limits related? Some sufficient conditions (reasonably easy to verify) which guarantee a positive answer to this question are given.",

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AB - The difficult problem of relating the large time behavior of the Navier-Stokes equations to the large time behavior of their Galerkin approximation is considered. Attention is restricted to the simplest situation dealing with stationary solutions and the question is the following one: if the computed approximation of the time dependent equations 'seems to converge' to some limit as approached t yields cent , is the same true for the exact problem and are the limits related? Some sufficient conditions (reasonably easy to verify) which guarantee a positive answer to this question are given.

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ON THE LARGE TIME GALERKIN APPROXIMATION OF THE NAVIER-STOKES EQUATIONS.

Abstract

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