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Elliott, CM and Ranner, T (2015) Evolving surface finite element method for the Cahn-Hilliard equation. Numerische Mathematik, 129 (3). pp. 483-534. ISSN 0029-599X
Abstract
We use the evolving surface finite element method to solve a Cahn- Hilliard equation on an evolving surface with prescribed velocity. We start by deriving the equation using a conservation law and appropriate transport for- mulae and provide the necessary functional analytic setting. The finite element method relies on evolving an initial triangulation by moving the nodes according to the prescribed velocity. We go on to show a rigorous well-posedness result for the continuous equations by showing convergence, along a subse- quence, of the finite element scheme. We conclude the paper by deriving error estimates and present various numerical examples.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2015, Springer. This is an author produced version of a paper published in Numerische Mathematik. Uploaded in accordance with the publisher's self-archiving policy. The final publication is available at Springer via http://dx.doi.org/10.1007/s00211-014-0644-y |
Keywords: | Evolving surface finite element method; Cahn-Hilliard equation; triangulated surfaces; error analysis |
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: | Symplectic Publications |
Date Deposited: | 10 Jun 2014 13:43 |
Last Modified: | 03 Dec 2020 19:01 |
Published Version: | http://dx.doi.org/10.1007/s00211-014-0644-y |
Status: | Published |
Publisher: | Springer Verlag |
Identification Number: | 10.1007/s00211-014-0644-y |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:79170 |
Available Versions of this Item
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Evolving surface finite element method for the Cahn-Hilliard equation. (deposited 22 Jan 2014 10:50)
- Evolving surface finite element method for the Cahn-Hilliard equation. (deposited 10 Jun 2014 13:43) [Currently Displayed]