Optimal convergence analysis of the virtual element methods for viscoelastic wave equations with variable coefficients on polygonal meshes

IF 16.4 1区 化学 Q1 CHEMISTRY, MULTIDISCIPLINARY
Gouranga Pradhan, Bhupen Deka
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引用次数: 0

Abstract

The objective of this work is to develop a conforming virtual element method for viscoelastic wave equations with variable coefficients on polygonal meshes. For problems where the coefficients are variable, the standard virtual element discrete forms do not work efficiently and require modification. For the optimal convergence estimate of the semi-discrete approximation in the \(L^{2}\) norm, a special projection operator is used. In the fully discrete scheme, the implicit second-order Newmark method is employed to approximate the temporal derivatives. Numerical experiments are presented to support the theoretical results. The proposed numerical algorithm can be applied to various problems arising in the engineering and medical fields.

Abstract Image

多边形网格上可变系数粘弹性波方程虚拟元素方法的最佳收敛分析
这项工作的目的是为多边形网格上系数可变的粘弹性波方程开发一种符合要求的虚拟元素方法。对于系数可变的问题,标准的虚拟元素离散形式无法有效工作,需要进行修改。为了在 \(L^{2}\) 规范下对半离散近似进行最佳收敛估计,使用了一种特殊的投影算子。在全离散方案中,采用了隐式二阶纽马克方法来逼近时间导数。为支持理论结果,我们进行了数值实验。所提出的数值算法可应用于工程和医学领域出现的各种问题。
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来源期刊
Accounts of Chemical Research
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.
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