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arXiv · 2210.06191

"Gradient-free" diffuse approximations of the Willmore functional and Willmore flow

Nils Dabrock·Sascha Knüttel·Matthias Röger
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Abstract

We introduce new diffuse approximations of the Willmore functional and the Willmore flow. They are based on a corresponding approximation of the perimeter that has been studied by Amstutz-van Goethem [{\em Interfaces Free Bound. 14 (2012)}]. We identify the candidate for the $\Gamma$--convergence, prove the $\Gamma$--limsup statement and justify the convergence to the Willmore flow by an asymptotic expansion. Furthermore, we present numerical simulations that are based on the new approximation.

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Nils Dabrock, Sascha Knüttel, Matthias Röger. 2022-10-12. "Gradient-free" diffuse approximations of the Willmore functional and Willmore flow. https://doi.org/10.3233/asy-221810

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