Uniformly HP-Stable Elements for the Elasticity Complex

IF 3.2 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Numerical Analysis Pub Date : 2026-05-27 DOI:10.1137/24m1701605

Francis R. A. Aznaran, Kaibo Hu, Charles Parker

引用次数: 0

Abstract

SIAM Journal on Numerical Analysis, Volume 64, Issue 3, Page 708-736, June 2026.
Abstract. For the discretization of symmetric, divergence-conforming stress tensors in continuum mechanics, we prove inf-sup stability bounds which are uniform in polynomial degree and mesh size for the Hu–Zhang finite element in two dimensions. This is achieved via an explicit construction of a bounded right inverse of the divergence operator, with the crucial component being the construction of bounded Poincaré operators for the stress elasticity complex which are polynomial-preserving, in the Bernstein–Gelfand–Gelfand framework of the finite element exterior calculus. We also construct [math]-bounded projection operators satisfying a commuting diagram property and [math]-stable Hodge decompositions. Numerical examples are provided.

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弹性配合物的均匀hp稳定元

SIAM数值分析杂志，64卷，第3期，708-736页，2026年6月。摘要。对于连续介质力学中对称散度一致性应力张量的离散化问题，我们证明了虎张有限元在二维上多项式次和网格尺寸是一致的稳定界。这是通过散度算子的有界右逆的显式构造来实现的，关键部分是在有限元外部演算的Bernstein-Gelfand-Gelfand框架中，为应力弹性复合体构造多项式保持的有界poincar算子。我们还构造了满足交换图性质的[数学]-有界投影算子和[数学]-稳定Hodge分解。给出了数值算例。

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

SIAM Journal on Numerical Analysis 数学-应用数学

CiteScore

4.80

自引率

6.90%

发文量

110

审稿时长

4-8 weeks

期刊介绍： SIAM Journal on Numerical Analysis (SINUM) contains research articles on the development and analysis of numerical methods. Topics include the rigorous study of convergence of algorithms, their accuracy, their stability, and their computational complexity. Also included are results in mathematical analysis that contribute to algorithm analysis, and computational results that demonstrate algorithm behavior and applicability.