Tangential Tensor Fields on Deformable Surfaces – How to Derive Consistent L2-Gradient Flows

Ingo Nitschke, Souhayl Sadik, Axel Voigt*

*Corresponding author for this work

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review

Abstract

We consider gradient flows of surface energies that depend on the surface by a parameterization and on a tangential tensor field. The flow allows for dissipation by evolving the parameterization and the tensor field simultaneously. This requires the choice of a notation for independence. We introduce different gauges of surface independence and show their consequences for the evolution. In order to guarantee a decrease in energy, the gauge of surface independence and the time derivative have to be chosen consistently. We demonstrate the results for a surface Frank–Oseen–Helfrich energy.

Original languageEnglish
JournalIMA Journal of Applied Mathematics
Volume88, 2023
Issue6
Pages (from-to)917-958
Number of pages42
ISSN1464-3634
DOIs
Publication statusPublished - Mar 2024

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