Mixed Finite Element Methods for Linear Cosserat Equations

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Numerical Analysis Pub Date : 2025-02-07 DOI:10.1137/24m1648387

W. M. Boon, O. Duran, J. M. Nordbotten

引用次数: 0

Abstract

SIAM Journal on Numerical Analysis, Volume 63, Issue 1, Page 306-333, February 2025.
Abstract. We consider the equilibrium equations for a linearized Cosserat material and provide two perspectives concerning well-posedness. First, the system can be viewed as the Hodge–Laplace problem on a differential complex. On the other hand, we show how the Cosserat materials can be analyzed by inheriting results from linearized elasticity. Both perspectives give rise to mixed finite element methods, which we refer to as strongly and weakly coupled, respectively. We prove convergence of both classes of methods, with particular attention to improved convergence rate estimates, and stability in the limit of vanishing characteristic length of the micropolar structure. The theoretical results are fully reflected in the actual performance of the methods, as shown by the numerical verifications.

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线性Cosserat方程的混合有限元方法

SIAM数值分析杂志，第63卷，第1期，306-333页，2025年2月。摘要。我们考虑了线性化的coserat材料的平衡方程，并提供了关于适定性的两种观点。首先，该系统可以看作是微分复上的霍奇-拉普拉斯问题。另一方面，我们展示了如何通过继承线性化弹性的结果来分析Cosserat材料。这两种观点都产生了混合有限元方法，我们分别称之为强耦合和弱耦合。我们证明了这两类方法的收敛性，特别注意改进的收敛率估计，以及在微极性结构特征长度消失极限下的稳定性。数值验证表明，理论结果充分反映在方法的实际性能中。

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.