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
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.
Metadata
Item Type: | Article |
---|---|
Authors/Creators: |
|
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 |
Dates: |
|
Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) |
Depositing User: | Repository Assistant |
Date Deposited: | 31 Oct 2006 |
Last Modified: | 28 Oct 2016 04:04 |
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: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:1658 |