Achieving Superconvergence by One-Dimensional Discontinuous Finite Elements: The CDG Method

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-06-01 DOI:10.4208/eajam.121021.200122

X. Ye, Shangyou Zhang

引用次数: 5

Abstract

. Novelty of this work is the development of a ﬁnite element method using discontinuous P k element, which has two-order higher convergence rate than the optimal order. The method is used to solve a one-dimensional second order elliptic problem. A totally new approach is developed for error analysis. Superconvergence of order two for the CDG ﬁnite element solution is obtained. The P k solution is lifted to an optimal order P k + 2 solution elementwise. The numerical results conﬁrm the theory.

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用一维间断有限元实现超收敛：CDG方法

这项工作的新颖之处在于开发了一种使用不连续Pk元的有限元方法，该方法的收敛速度比最优阶高两阶。该方法用于求解一维二阶椭圆问题。开发了一种全新的误差分析方法。得到了CDG有限元解的二阶超收敛性。将Pk解提升到最优阶Pk+2解。数值结果证实了这一理论。

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

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.