Baines, M.J., Hubbard, M.E., Jimack, P.K. et al. (1 more author) (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
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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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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 |
Dates: |
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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: | 13 Dec 2006 |
Last Modified: | 26 Oct 2016 11:50 |
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: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:1784 |