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A moving mesh finite element algorithm for the adaptive solution of time-dependent partial differential equations with moving boundaries

Baines, M.J., Hubbard, M.E. and Jimack, P.K. (2005) A moving mesh finite element algorithm for the adaptive solution of time-dependent partial differential equations with moving boundaries. Applied Numerical Mathematics, 54 (3-4). pp. 450-469. ISSN 0168-9274

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Abstract

A moving mesh finite element algorithm is proposed for the adaptive solution of nonlinear diffusion equations with moving boundaries in one and two dimensions. The moving mesh equations are based upon conserving a local proportion, within each patch of finite elements, of the total “mass” that is present in the projected initial data. The accuracy of the algorithm is carefully assessed through quantitative comparison with known similarity solutions, and its robustness is tested on more general problems.

Applications are shown to a variety of problems involving time-dependent partial differential equations with moving boundaries. Problems which conserve mass, such as the porous medium equation and a fourth order nonlinear diffusion problem, can be treated by a simplified form of the method, while problems which do not conserve mass require the full theory.

Item Type: Article
Copyright, Publisher and Additional Information: © 2004 IMACS. This is an author produced version of a paper published in 'Applied Numerical Mathematics'.
Keywords: Lagrangian meshes
Academic Units: The University of Leeds > Faculty of Engineering (Leeds) > School of Computing (Leeds)
Depositing User: Repository Assistant
Date Deposited: 14 Dec 2006
Last Modified: 08 Feb 2013 17:03
Published Version: http://dx.doi.org/10.1016/j.apnum.2004.09.013
Status: Published
Publisher: Elsevier B.V.
Refereed: Yes
Identification Number: 10.1016/j.apnum.2004.09.013
Related URLs:
URI: http://eprints.whiterose.ac.uk/id/eprint/1764

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