Unconditional energy stability and maximum principle preserving scheme for the Allen-Cahn equation

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-07-12 DOI:10.1007/s11075-024-01880-2

Zhuangzhi Xu, Yayun Fu

引用次数: 0

Abstract

In this paper, we propose a novel fully implicit numerical scheme that satisfies both nonlinear energy stability and maximum principle for the space fractional Allen-Cahn equation. Especially, the fully implicit second-order scheme in time has never been proved to preserve the maximum principle before. For the resulting nonlinear scheme, we also propose a nonlinear iterative algorithm, which is uniquely solvable, convergent, and can preserve discrete maximum principle in each iterative step. Then we provide an error estimate by using the established maximum principle which plays a key role in the analysis. Several numerical experiments are presented to verify the theoretical results.

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艾伦-卡恩方程的无条件能量稳定性和最大原则保持方案

在本文中，我们提出了一种新颖的全隐式数值方案，它同时满足空间分数 Allen-Cahn 方程的非线性能量稳定性和最大值原理。尤其是时间上的全隐式二阶方案，在此之前从未被证明能保持最大原则。对于由此产生的非线性方案，我们还提出了一种非线性迭代算法，该算法唯一可解、收敛，并能在每一步迭代中保留离散最大原则。然后，我们利用已建立的最大值原理提供了误差估计，这在分析中起到了关键作用。我们给出了几个数值实验来验证理论结果。

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.