三维的有限元de Rham和Stokes复合体

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Mathematics of Computation Pub Date : 2023-06-07 DOI:10.1090/mcom/3859

Long Chen, Xuehai Huang

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引用次数: 2

摘要

本文系统地构造了三维不同光滑度的有限元de Rham复合体和有限元Stokes复合体。通过简单晶格的非重叠分解，导出了三维光滑标量有限元。H(div) H(\operatorname {div})符合有限元和H(curl) H(\operatorname {curl})符合不同光滑度的有限元是在这些光滑标量有限元的基础上设计的。由这些单元导出了具有相应光滑性和交换图的有限元de Rham复合体。建立了H(div) H(\operatorname {div}) -符合有限元的div稳定性，并证明了这些有限元复合体的准确性。

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Finite element de Rham and Stokes complexes in three dimensions

Finite element de Rham complexes and finite element Stokes complexes with varying degrees of smoothness in three dimensions are systematically constructed in this paper. Smooth scalar finite elements in three dimensions are derived through a non-overlapping decomposition of the simplicial lattice. H ( div ) H(\operatorname {div}) -conforming finite elements and H ( curl ) H(\operatorname {curl}) -conforming finite elements with varying degrees of smoothness are devised based on these smooth scalar finite elements. The finite element de Rham complexes with corresponding smoothness and commutative diagrams are induced by these elements. The div stability of the H ( div ) H(\operatorname {div}) -conforming finite elements is established, and the exactness of these finite element complexes is proven.

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来源期刊

Mathematics of Computation 数学-应用数学

CiteScore

3.90

自引率

5.00%

发文量

审稿时长

7.0 months

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to research articles of the highest quality in computational mathematics. Areas covered include numerical analysis, computational discrete mathematics, including number theory, algebra and combinatorics, and related fields such as stochastic numerical methods. Articles must be of significant computational interest and contain original and substantial mathematical analysis or development of computational methodology.