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Optimal eigenvalue and asymtotic large-time approximations using the moving finite-element method

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This is a repository copy of

Optimal eigenvalue and asymtotic large-time approximations

using the moving finite-element method

.

White Rose Research Online URL for this paper:

http://eprints.whiterose.ac.uk/1658/

Article:

Jimack, P.K. (1996) Optimal eigenvalue and asymtotic large-time approximations using the

moving finite-element method. IMA Journal of Numerical Analysis, 16 (3). pp. 381-398.

ISSN 0272-4979

https://doi.org/10.1093/imanum/16.3.381

[email protected]

https://eprints.whiterose.ac.uk/

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White Rose Consortium ePrints Repository

http://eprints.whiterose.ac.uk/

This is an author produced version of a chapter published in IMA Journal of

Numerical Analysis.

White Rose Repository URL for this paper:

http://eprints.whiterose.ac.uk/1658/

Published as

Jimack, P.K. (1996) Optimal eigenvalue and asymtotic large-time approximations

using the moving finite-element method. IMA Journal of Numerical Analysis, 16

(3). pp. 381-398.

(3)

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ˆ~k~l•*ˆ&‘ƒ‚G–‚*„ˆû*‰‹~lœ*ˆí–—‘Œ0‹‰™Ž<û~V‚ 1ûG/û ˆ~;hœ*œ*”~‘G–—hˆ‰ˆû*‰†Ž<—‘ŒÄŒ–‰™Žíˆ!‰&ƒ„l‰Q‚G€_‘Œƒ’*‰å~l”n‰l’dˆ<ƒ~l‚wý-Gþ

(17)

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!1ûG/ûÿG‰™‘ŒÏŽ

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”`Ž<ˆŽ<ˆ/‰Qœ;ˆ~h”`ÿ*ŽÞ’*‚ÿG‰Q”`Ž<ˆ`h‚ÿVƒ‚*„kˆû*‰nˆ/‰Q‹œ~l”&‘Œ>œ*”~lœ‰Q”/ˆ<ƒ‰™Ž~.ˆû*‰n‹‰Qˆ/û*~¨ÿ å~l”œh”&h•~hŒÄnœ*”/~l•GŒƒ‰Q†Ž

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ƒ‚Lˆ/~ì &~l’*‚Lˆ1ˆû*‰n’Ž<‰n~=œb‰Q‚‘Œƒˆ ä’*‚ &ˆ<ƒ~l‚Žî~°ˆ/û*‰üŽ<~V”ˆ$œ*”~lœ~GŽ<‰™ÿ—• k}ÄŒCŒƒ‰Q”ý åþ& 1ûG/ûZd”‰üÿG‰™ŽÛ–„V‚*‰™ÿkˆ~

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û*~$‰Q€l‰Q” $ÄŒÄŒ>•‰ˆ~‹ÿG‰™‘Œ ˆ/û $ÏÿG‰Q”œ*”/~l•GŒƒ‰Q /ŒÏlŽ/Ž<‰™ŽQ*Ž<’ /û;lŽ.‚*~l‚GŒÄƒ‚*‰™h”œd”`h•~dŒC‰V’hˆ<ƒ~l‚ŽA~l”$Ž ¨Žíˆ‰Q†ŽQ

h‚ÿˆ~!•b‰Qˆˆ‰Q”$’*‚ÿG‰Q”`Ž<ˆ&h‚ÿ—ˆû*‰•‰Qû‘€lƒ~l’*”1~>ˆû*‰X‰™Ž<û ÿG’*”큖‚*„ˆû*‰ƒ‚Gƒˆ<Ï‘Œ.ˆ”`h‚ŽÛ–‰Q‚Gˆ`ŽQV”`hˆû*‰Q”$ˆûd‚ <’Ž<ˆ å~l”

ŒÏh”„l‰nˆí–‰™Ž

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û‘€l‰•b‰Q‰Q‚ Q‘Œ&’GŒÏhˆ‰™ÿ—‰&*ˆ”‰Q‰&Œ—&’*”`hˆ‰&Œ lGˆ~ÿG‰/–—‘Œ>œGŒ¬ &‰™ŽQ ä”~V nœ*”&&ˆ<Q‘ŒEœb~hƒ‚Lˆ$~>€Vƒ‰ ˆ/û*‰Q”‰$ÏŽ

‚*~‚*‰Q‰™ÿ¶ˆ~”‰V’Gƒ”‰$ˆû*‰.‹‰™Ž<û¶Œ–~Qhˆ<ƒ~l‚Žˆ/~îŽí’ ûûG–„Vûì &’*”` ýȉ™Ž<œ‰/Ï‘ŒÄŒ ‚L’*‹‰Q”íQ_Œ V’lÿG”`hˆ/’*”‰ÏŽ>•b‰&–‚*„

’Ž<‰™ÿbþú$û*‰$‚*~¨ÿG‰$œb~hƒ‚Lˆ`އ‰Q€l~hŒƒ€l‰A€l‰Q”+V’GVŒ 2ˆ/~$ƒˆûGƒ‚†$€l‰Q” !Ž<†‘ŒÄŒÿV¬Žíˆ`h‚ &‰$~ˆû*‰&ƒ”‚‘ŒLœb~LŽÒƒˆ<ƒ~l‚†d‚ÿ!Ž<~

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References

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