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

IF 1.9 4区 数学 Q1 MATHEMATICS
Yaru Liu,Yinnian He, Xinlong Feng
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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
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。
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来源期刊
CiteScore
2.80
自引率
7.70%
发文量
33
审稿时长
>12 weeks
期刊介绍: Numerical Mathematics: Theory, Methods and Applications (NM-TMA) publishes high-quality original research papers on the construction, analysis and application of numerical methods for solving scientific and engineering problems. Important research and expository papers devoted to the numerical solution of mathematical equations arising in all areas of science and technology are expected. The journal originates from the journal Numerical Mathematics: A Journal of Chinese Universities (English Edition). NM-TMA is a refereed international journal sponsored by Nanjing University and the Ministry of Education of China. As an international journal, NM-TMA is published in a timely fashion in printed and electronic forms.
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