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arXiv · 2209.13272

Tangential Tensor Fields on Deformable Surfaces -- How to Derive Consistent $L^2$-Gradient Flows

Ingo Nitschke·Souhayl Sadik·Axel Voigt
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Abstract

We consider gradient flows of surface energies which 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-Hilfrich energy.

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Ingo Nitschke, Souhayl Sadik, Axel Voigt. 2022-09-27. Tangential Tensor Fields on Deformable Surfaces -- How to Derive Consistent $L^2$-Gradient Flows. https://arxiv.org/abs/2209.13272

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