Hamilton-Jacobi equations on an evolving surface

Deckelnick, Klaus, Elliott, Charles M, Miura, Tatsu-Hiko and Styles, Vanessa (2019) Hamilton-Jacobi equations on an evolving surface. Mathematics of Computation. ISSN 0025-5718

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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 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.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Research Centres and Groups: Numerical Analysis and Scientific Computing Research Group
Subjects: Q Science > QA Mathematics
Depositing User: Alice Jackson
Date Deposited: 07 Jan 2019 13:07
Last Modified: 16 Apr 2019 11:15
URI: http://sro.sussex.ac.uk/id/eprint/81088

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Project NameSussex Project NumberFunderFunder Ref
Grant-in-Aid for JSPS FellowsUnsetUnset16J02664
Wolfson research merit awardG0647ROYAL SOCIETYUnset