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Hamilton-Jacobi equations on an evolving surface
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Deckelnick, Klaus, Elliott, Charles M., Miura, Tatsu-Hiko and Styles, Vanessa (2019) Hamilton-Jacobi equations on an evolving surface. Mathematics of Computation, 88 . pp. 2635-2664. doi:10.1090/mcom/3420 ISSN 0025-5718.
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WRAP-Hamilton-Jocobi-equations-evolving-Elliott-2018.pdf - Accepted Version - Requires a PDF viewer. Download (961Kb) | Preview |
Official URL: https://doi.org/10.1090/mcom/3420
Abstract
We consider the well-posedness and numerical approximation of a Hamilton–Jacobi equation on an evolving hypersurface in R3. Definitions of viscosity sub- and super solutions are extended in a natural way to evolving hypersurfaces and provide uniqueness by comparison. An explicit in time monotone numerical approximation is derived on evolving interpolating triangulated surfaces. The scheme relies on a finite volume discretisation which does not require acute triangles. The scheme is shown to be stable and consistent leading to an existence proof via the proof of convergence. Finally an error bound is proved of the same order as in the flat stationary case.
| Item Type: | Journal Article | ||||||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||||
| Library of Congress Subject Headings (LCSH): | Hypersurfaces, Hamilton-Jacobi equations | ||||||||||||
| Journal or Publication Title: | Mathematics of Computation | ||||||||||||
| Publisher: | American Mathematical Society | ||||||||||||
| ISSN: | 0025-5718 | ||||||||||||
| Official Date: | 26 March 2019 | ||||||||||||
| Dates: |
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| Volume: | 88 | ||||||||||||
| Page Range: | pp. 2635-2664 | ||||||||||||
| DOI: | 10.1090/mcom/3420 | ||||||||||||
| Status: | Peer Reviewed | ||||||||||||
| Publication Status: | Published | ||||||||||||
| Reuse Statement (publisher, data, author rights): | First published in Mathematics of Computation in 88 . pp. 2635-2664 published by the American Mathematical Society. © Copyright 2019 American Mathematical Society | ||||||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||||||
| Copyright Holders: | American Mathematical Society | ||||||||||||
| Date of first compliant deposit: | 17 December 2018 | ||||||||||||
| Date of first compliant Open Access: | 30 January 2019 | ||||||||||||
| RIOXX Funder/Project Grant: |
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