A balanced finite-element method for an axisymmetrically loaded thin shell

IF 0.6 4区数学 Q4 MATHEMATICS, APPLIED

Applications of Mathematics Pub Date : 2024-01-30 DOI:10.21136/AM.2024.0134-23

Norbert Heuer, Torsten Linss

引用次数: 0

Abstract

We analyse a finite-element discretisation of a differential equation describing an axisymmetrically loaded thin shell. The problem is singularly perturbed when the thickness of the shell becomes small. We prove robust convergence of the method in a balanced norm that captures the layers present in the solution. Numerical results confirm our findings.

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轴对称加载薄壳的平衡有限元法

我们分析了描述轴对称负载薄壳的微分方程的有限元离散化。当壳的厚度变小时，问题会受到奇异扰动。我们证明了该方法在平衡规范下的稳健收敛性，该规范捕捉到了解中存在的层。数值结果证实了我们的发现。

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

Applications of Mathematics 数学-应用数学

CiteScore

1.50

自引率

0.00%

发文量

审稿时长

3.0 months

期刊介绍： Applications of Mathematics publishes original high quality research papers that are directed towards applications of mathematical methods in various branches of science and engineering. The main topics covered include: - Mechanics of Solids; - Fluid Mechanics; - Electrical Engineering; - Solutions of Differential and Integral Equations; - Mathematical Physics; - Optimization; - Probability Mathematical Statistics. The journal is of interest to a wide audience of mathematicians, scientists and engineers concerned with the development of scientific computing, mathematical statistics and applicable mathematics in general.