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Consistent dirichlet boundary conditions for numerical solution of moving boundary problems

Hubbard, M.E., Baines, M.J. and Jimack, P.K. (2009) Consistent dirichlet boundary conditions for numerical solution of moving boundary problems. Applied Numerical Mathematics, 59 (6). pp. 1337-1353. ISSN 01689274

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Abstract

We consider the imposition of Dirichlet boundary conditions in the finite element mod-elling of moving boundary problems in one and two dimensions for which the total mass is prescribed. A modification of the standard linear finite element test space allows the boundary conditions to be imposed strongly whilst simultaneously conserving a discrete mass. The validity of the technique is assessed for a specific moving mesh finite element method, although the approach is more general. Numerical comparisons are carried out for mass-conserving solutions of the porous medium equation with Dirichlet boundary conditions and for a moving boundary problem with a source term and time-varying mass.

Item Type: Article
Copyright, Publisher and Additional Information: Copyright © 2008 IMACS Published by Elsevier B.V. This is an author produced version of a paper published in 'Applied Numerical Mathematics'. Uploaded in accordance with the publisher's self-archiving policy.
Institution: The University of Leeds
Academic Units: The University of Leeds > Faculty of Engineering (Leeds) > School of Computing (Leeds)
Depositing User: Miss Jamie Grant
Date Deposited: 02 Apr 2009 14:44
Last Modified: 07 Jun 2014 06:50
Published Version: http://dx.doi.org/10.1016/j.apnum.2008.08.002
Status: Published
Publisher: Elsevier
Refereed: Yes
Identification Number: 10.1016/j.apnum.2008.08.002
Related URLs:
URI: http://eprints.whiterose.ac.uk/id/eprint/8483

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