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Elliott, CM and Ranner, T (2013) Evolving surface finite element method for the Cahn-Hilliard equation. (Unpublished)
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 accord- ing 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: | © 2013 authors. Imported from arXiv |
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) > Institute for Computational and Systems Science (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 22 Jan 2014 10:50 |
Last Modified: | 15 Sep 2014 01:31 |
Status: | Unpublished |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:76693 |
Available Versions of this Item
- Evolving surface finite element method for the Cahn-Hilliard equation. (deposited 22 Jan 2014 10:50) [Currently Displayed]