A diffuse interface approach for vector-valued PDEs on surfaces

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-07-18 DOI:10.4310/cms.2024.v22.n6.a13

Michael Nestler, Axel Voigt

引用次数: 0

Abstract

Approximating PDEs on surfaces by the diffuse interface approach allows us to use standard numerical tools to solve these problems. This makes it an attractive numerical approach. We extend this approach to vector-valued surface PDEs and explore their convergence properties. In contrast to the well-studied case of scalar-valued surface PDEs, the optimal order of convergence can only be achieved if certain higher-order relations between mesh size and interface width are fulfilled. This difference results from the increased coupling between the surface geometry and the PDE for vector-valued quantities defined on it.

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表面上矢量值 PDE 的扩散界面方法

用扩散界面方法来逼近表面上的 PDEs，可以让我们使用标准的数值工具来解决这些问题。这使它成为一种有吸引力的数值方法。我们将这种方法扩展到矢量值曲面 PDE，并探索其收敛特性。与研究得很透彻的标量值曲面 PDEs 不同，只有在网格尺寸和界面宽度之间的某些高阶关系得到满足时，才能达到最佳收敛阶数。这种差异源于表面几何与定义在其上的矢量值量的 PDE 之间的耦合增加。

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

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.