先进型分段连续双曲型偏微分方程galerkin有限元法的收敛性和稳定性

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-09-04 DOI:10.3846/mma.2023.16677

Yongtang Chen, Qi Wang

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引用次数: 0

摘要

本文研究了一类具有分段连续参数的双曲型偏微分方程的Galerkin有限元法的收敛性和稳定性。首先用分离变量法得到了解析解的表达式，然后得到了稳定性的充分条件。利用Galerkin有限元法导出了半离散格式和全离散格式，并分析了它们在l2范数下的收敛性。此外，还研究了两种方案的稳定性。半离散格式可以实现无条件稳定。给出了完全离散格式稳定性的充分条件，在此条件下解析解是渐近稳定的。最后通过数值实验对理论结果进行了验证。

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CONVERGENCE AND STABILITY OF GALERKIN FINITE ELEMENT METHOD FOR HYPERBOLIC PARTIAL DIFFERENTIAL EQUATION WITH PIECEWISE CONTINUOUS ARGUMENTS OF ADVANCED TYPE

This paper deals with the convergence and stability of Galerkin finite element method for a hyperbolic partial differential equations with piecewise continuous arguments of advanced type. First of all, we obtain the expression of analytic solution by the method of separation variable, then the sufficient conditions for stability are obtained. Semidiscrete and fully discrete schemes are derived by Galerkin finite element method, and their convergence are both analyzed in L2-norm. Moreover, the stability of the two schemes are investigated. The semidiscrete scheme can achieve unconditionally stability. The sufficient conditions of stability for fully discrete scheme are derived under which the analytic solution is asymptotically stable. Finally, some numerical experiments are presented to illustrate the 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.