__smbhome.uscs.susx.ac.uk_akj23_Documents_HJ On Evolving Surface.pdf (686.64 kB)
Hamilton-Jacobi equations on an evolving surface
journal contribution
posted on 2023-06-09, 16:22 authored by Klaus Deckelnick, Charles M Elliott, Tatsu-Hiko Miura, Vanessa StylesVanessa StylesWe consider the well-posedness and numerical approximation of a Hamilton-Jacobi equation on an evolving hypersurface in R3. Definitions of viscosity sub- and supersolutions 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 at stationary case.
Funding
Grant-in-Aid for JSPS Fellows; 16J02664
Wolfson research merit award; G0647; ROYAL SOCIETY
History
Publication status
- Published
File Version
- Accepted version
Journal
Mathematics of ComputationISSN
0025-5718Publisher
American Mathematical SocietyExternal DOI
Department affiliated with
- Mathematics Publications
Research groups affiliated with
- Numerical Analysis and Scientific Computing Research Group Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2019-01-07First Open Access (FOA) Date
2019-01-28First Compliant Deposit (FCD) Date
2019-01-02Usage metrics
Categories
No categories selectedKeywords
Licence
Exports
RefWorks
BibTeX
Ref. manager
Endnote
DataCite
NLM
DC