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

Full text available as:

Text
Jimackp5_Jimack96a.pdf
Available under License : See the attached licence file.
Download (300Kb)

Published Version: http://dx.doi.org/10.1093/imanum/16.3.381

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
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:	08 Feb 2013 17:06
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:	http://www.comp.leeds.ac.uk/pkj/publicat...
URI:	http://eprints.whiterose.ac.uk/id/eprint/1658

Actions (login required)

View Item