任意维$$C^r$$共形有限元空间的构造

IF 2.5 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Foundations of Computational Mathematics Pub Date : 2023-10-17 DOI:10.1007/s10208-023-09627-6

Jun Hu, Ting Lin, Qingyu Wu

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引用次数: 1

摘要

本文提出了一个在任意维上具有任意r的\（C^r）相容有限元空间的构造。结果表明，如果\（k\ge 2^{d}r+1\）次多项式的空间\（\mathcal｛P｝｝_k\）可以作为d维有限元空间的形状函数空间。这是第一个以统一的方式在任何维度上构造这种符合C^r的有限元的工作。

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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A Construction of $$C^r$$ Conforming Finite Element Spaces in Any Dimension

This paper proposes a construction of $C^r$ conforming finite element spaces with arbitrary r in any dimension. It is shown that if $k \ge 2^{d}r+1$ the space ${\mathcal {P}}_k$ of polynomials of degree $\le k$ can be taken as the shape function space of $C^r$ finite element spaces in d dimensions. This is the first work on constructing such $C^r$ conforming finite elements in any dimension in a unified way.

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来源期刊

Foundations of Computational Mathematics 数学-计算机：理论方法

CiteScore

6.90

自引率

3.30%

发文量

审稿时长

>12 weeks

期刊介绍： Foundations of Computational Mathematics (FoCM) will publish research and survey papers of the highest quality which further the understanding of the connections between mathematics and computation. The journal aims to promote the exploration of all fundamental issues underlying the creative tension among mathematics, computer science and application areas unencumbered by any external criteria such as the pressure for applications. The journal will thus serve an increasingly important and applicable area of mathematics. The journal hopes to further the understanding of the deep relationships between mathematical theory: analysis, topology, geometry and algebra, and the computational processes as they are evolving in tandem with the modern computer. With its distinguished editorial board selecting papers of the highest quality and interest from the international community, FoCM hopes to influence both mathematics and computation. Relevance to applications will not constitute a requirement for the publication of articles. The journal does not accept code for review however authors who have code/data related to the submission should include a weblink to the repository where the data/code is stored.