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

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

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Abstract

The moving finite-element method for the solution of time-dependent partial differential equations is a numerical solution scheme which allows the automatic adaptation of the finite-element approximation space with time, through the use of mesh relocation (r-refinement).

This paper analyzes the asymptotic behaviour of the method for large times when it is applied to the solution of a class of self-adjoint parabolic equations in an arbitrary number of space dimensions. It is shown that asymptotically the method will produce solutions which converge to a fixed mesh and it is proved that such a mesh allows an optimal approximation of the slowest-decaying eigenvalue and eigenfunction for the problem. Hence it is demonstrated that the moving finite-element method can yield an optimal solution to such parabolic problems for large times.

Item Type: Article
Copyright, Publisher and Additional Information: © 1996 by Institute of Mathematics and its Applications. This is an author produced version of a paper published in 'IMA Journal of Numerical Analysis'
Keywords: moving finite elements, eigenvalue problems, best free knot approximations
Institution: The University of Leeds
Academic Units: The University of Leeds > Faculty of Engineering (Leeds) > School of Computing (Leeds)
Depositing User: Repository Assistant
Date Deposited: 31 Oct 2006
Last Modified: 06 Jun 2014 18:34
Published Version: http://dx.doi.org/10.1093/imanum/16.3.381
Status: Published
Publisher: Oxford University Press
Refereed: Yes
Identification Number: 10.1093/imanum/16.3.381
Related URLs:
URI: http://eprints.whiterose.ac.uk/id/eprint/1658

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