“Gradient-free” diffuse approximations of the Willmore functional and Willmore flow

IF 1.1 4区数学 Q2 MATHEMATICS, APPLIED

Asymptotic Analysis Pub Date : 2022-10-07 DOI:10.3233/ASY-221810

Nils Dabrock, Sascha Knuttel, M. Roger

引用次数: 0

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 [Interfaces Free Bound. 14 (2012)]. We identify the candidate for the Γ-convergence, prove the Γ-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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Willmore泛函和Willmore流的“无梯度”扩散近似

我们引入了Willmore泛函和Willmore流的新的扩散近似。它们基于Amstutz-van Goethem [interface Free Bound. 14(2012)]研究的周长的相应近似。我们确定了Γ-convergence的候选者，证明了Γ-limsup命题，并通过渐近展开式证明了其收敛于Willmore流。此外，我们给出了基于新近似的数值模拟。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Asymptotic Analysis 数学-应用数学

CiteScore

1.90

自引率

7.10%

发文量

审稿时长

6 months

期刊介绍： The journal Asymptotic Analysis fulfills a twofold function. It aims at publishing original mathematical results in the asymptotic theory of problems affected by the presence of small or large parameters on the one hand, and at giving specific indications of their possible applications to different fields of natural sciences on the other hand. Asymptotic Analysis thus provides mathematicians with a concentrated source of newly acquired information which they may need in the analysis of asymptotic problems.