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Scale-invariant moving finite elements for nonlinear partial differential equations in two dimensions

Baines, M.J., Hubbard, M.E., Jimack, P.K. and Jones, A.C. (2006) Scale-invariant moving finite elements for nonlinear partial differential equations in two dimensions. Applied Numerical Mathematics, 56 (2). pp. 230-252. ISSN 0168-9274

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Abstract

A scale-invariant moving finite element method is proposed for the adaptive solution of nonlinear partial differential equations. The mesh movement is based on a finite element discretisation of a scale-invariant conservation principle incorporating a monitor function, while the time discretisation of the resulting system of ordinary differential equations is carried out using a scale-invariant time-stepping which yields uniform local accuracy in time.

The accuracy and reliability of the algorithm are successfully tested against exact self-similar solutions where available, and otherwise against a state-of-the-art h-refinement scheme for solutions of a two-dimensional porous medium equation problem with a moving boundary. The monitor functions used are the dependent variable and a monitor related to the surface area of the solution manifold.

Item Type: Article
Copyright, Publisher and Additional Information: © 2005 IMACS. This is an author produced version of a paper published in 'Applied Numerical Mathematics'.
Keywords: Scale invariance, Moving meshes, Finite element method, Porous medium equation, Moving boundaries
Academic Units: The University of Leeds > Faculty of Engineering (Leeds) > School of Computing (Leeds)
Depositing User: Repository Assistant
Date Deposited: 13 Dec 2006
Last Modified: 08 Feb 2013 17:03
Published Version: http://dx.doi.org/10.1016/j.apnum.2005.04.002
Status: Published
Publisher: Elsevier B.V.
Refereed: Yes
Identification Number: 10.1016/j.apnum.2005.04.002
Related URLs:
URI: http://eprints.whiterose.ac.uk/id/eprint/1784

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