任意余维平均曲率流的收敛有限元算法

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-07-22 DOI:10.4171/ifb/493

Tim Binz, Bal'azs Kov'acs

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引用次数: 2

摘要

给出了任意高余维曲面平均曲率流的半离散化和完全离散化的最优阶一致时间H^1范数误差估计。所提出和研究的数值方法是基于一个抛物线系统，将表面流耦合到平均曲率矢量和切空间正交投影的演化方程中。该算法采用演化曲面有限元和线性隐式后向差分公式。对于多项式次以上的有限元和2 ~ 5阶的后向差分公式，该数值方法允许收敛分析。余维2的数值实验说明并补充了我们的理论结果。

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A convergent finite element algorithm for mean curvature flow in arbitrary codimension

Optimal-order uniform-in-time $H^1$-norm error estimates are given for semi- and full discretizations of mean curvature flow of surfaces in arbitrarily high codimension. The proposed and studied numerical method is based on a parabolic system coupling the surface flow to evolution equations for the mean curvature vector and for the orthogonal projection onto the tangent space. The algorithm uses evolving surface finite elements and linearly implicit backward difference formulae. This numerical method admits a convergence analysis in the case of finite elements of polynomial degree at least two and backward difference formulae of orders two to five. Numerical experiments in codimension 2 illustrate and complement our theoretical results.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.