A discrete elasticity complex on three-dimensional Alfeld splits

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Numerische Mathematik Pub Date : 2023-11-30 DOI:10.1007/s00211-023-01381-9

Snorre H. Christiansen, Jay Gopalakrishnan, Johnny Guzmán, Kaibo Hu

引用次数: 15

Abstract

We construct conforming finite element elasticity complexes on the Alfeld splits of tetrahedra. The complex consists of vector fields and symmetric tensor fields, interlinked via the linearized deformation operator, the linearized curvature operator, and the divergence operator, respectively. The construction is based on an algebraic machinery that derives the elasticity complex from de Rham complexes, and smoother finite element differential forms.

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三维Alfeld分裂上的离散弹性复合体

在四面体的Alfeld分裂上构造了合型有限元弹性复合体。复合体由向量场和对称张量场组成，分别通过线性化变形算子、线性化曲率算子和散度算子相互连接。该结构基于一种代数机制，该机制从de Rham复合体中衍生出弹性复合体，以及更平滑的有限元微分形式。

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

Numerische Mathematik 数学-应用数学

CiteScore

4.10

自引率

4.80%

发文量

审稿时长

6-12 weeks

期刊介绍： Numerische Mathematik publishes papers of the very highest quality presenting significantly new and important developments in all areas of Numerical Analysis. "Numerical Analysis" is here understood in its most general sense, as that part of Mathematics that covers: 1. The conception and mathematical analysis of efficient numerical schemes actually used on computers (the "core" of Numerical Analysis) 2. Optimization and Control Theory 3. Mathematical Modeling 4. The mathematical aspects of Scientific Computing