单边接触问题的 HDG 方法

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-07-25 DOI:10.1186/s13660-024-03175-5

Mingyang Zhao, Liangjin Zhou

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引用次数: 0

摘要

本文利用正则化方法和迭代程序，提出了单边接触问题的 HDG 近似解。在我们的研究中，u 代表势（弹性体的位移），q 代表通量（施加在弹性体上的力）。我们的分析表明，使用度数为 $k (k \ge 1)$ 的多项式可使 u 和 q 在 $L^{2}$ -norm（L^{2}$ 正态）下达到最佳收敛率 $k+1$。数值结果与理论研究结果一致，凸显了针对单边接触问题提出的 HDG 近似方法的有效性和可靠性。

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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HDG methods for the unilateral contact problem

This article presents the HDG approximation as a solution to the unilateral contact problem, leveraging the regularization method and an iterative procedure for resolution. In our study, u represents the potential (displacement of the elastic body) and q represents the flux (the force exerted on the body). Our analysis establishes that the utilization of polynomials of degree $k (k \ge 1)$ leads to achieving an optimal convergence rate of order $k+1$ in $L^{2}$ -norm for both u and q. Importantly, this optimal convergence is maintained irrespective of whether the domain is discretized through a structured or unstructured grid. The numerical results consistently align with the theoretical findings, underscoring the effectiveness and reliability of the proposed HDG approximation method for unilateral contact problems.

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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.