Stability and Convergence of the Integral-Averaged Interpolation Operator Based on $Q_1$-element in $\mathbb{R}^n$

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-05-01 DOI:10.4208/nmtma.oa-2023-0122

Yaru Liu,Yinnian He, Xinlong Feng

引用次数: 0

Abstract

In this paper, we propose an integral-averaged interpolation operator $I_\tau$ in a bounded domain $Ω ⊂ \mathbb{R}^n$ by using $Q_1$-element. The interpolation coefficient is defined by the average integral value of the interpolation function $u$ on the interval formed by the midpoints of the neighboring elements. The operator $I_\tau$ reduces the regularity requirement for the function $u$ while maintaining standard convergence. Moreover, it possesses an important property of $||I_\tau u||_{0,Ω} ≤ ||u||_{0,Ω}.$ We conduct stability analysis and error estimation for the operator $I\tau.$ Finally, we present several numerical examples to test the efficiency and high accuracy of the operator

查看原文本刊更多论文

基于 $\mathbb{R}^n$ 中 $Q_1$ 元素的积分平均插值算子的稳定性和收敛性

本文通过使用 $Q_1$ 元素，在有界域 $Ω ⊂ \mathbb{R}^n$ 中提出了一种积分平均插值算子 $I_\tau$。插值系数由插值函数 $u$ 在由相邻元素中点构成的区间上的平均积分值定义。算子 $I_\tau$ 在保持标准收敛性的同时，降低了对函数 $u$ 的正则性要求。此外，它还具有一个重要的性质，即 $||I_\tau u||_{0,Ω} ≤ ||u||_{0,Ω}.

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

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.