二维线性弹性浅壳方程中不符元素的新先验误差估计

IF 1.2 4区 数学 Q2 MATHEMATICS, APPLIED
Rongfang Wu, Xiaoqin Shen, Qian Yang, Shengfeng Zhu
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引用次数: 0

摘要

本文主要针对二维线性弹性浅壳方程提出了一种新的先验误差估计方法,该方法依赖于基尔霍夫-洛夫理论族。由于中面上各点的位移分量具有不同的规律性,因此分析了离散化浅壳方程的非符合元素。然后,依靠富集算子,在任意 $m \gt 0$ 的正则假设 $\vec{\zeta}_H \times \zeta_3 \in (H^{1+m} (\omega))^2 \times H^{2+m} (\omega)$ 下给出了能量规范的新误差估计。与其他壳文献中的经典误差分析相比,数值解的收敛阶数可以由其对应的近似误差以任意高阶项来控制,这填补了计算壳理论的空白。最后,鞍形壳和圆柱形壳的数值结果证实了理论预测。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A new priori error estimation of nonconforming element for two-dimensional linearly elastic shallow shell equations
In this paper, we mainly propose a new priori error estimation for the two-dimensional linearly elastic shallow shell equations, which rely on a family of Kirchhoff–Love theories. As the displacement components of the points on the middle surface have different regularities, the nonconforming element for the discretization shallow shell equations is analysed. Then, relying on the enriching operator, a new error estimate of energy norm is given under the regularity assumption $\vec{\zeta}_H \times \zeta_3 \in (H^{1+m} (\omega))^2 \times H^{2+m} (\omega)$ with any $m \gt 0$. Compared with the classic error analysis in other shell literature, convergence order of numerical solution can be controlled by its corresponding approximation error with an arbitrarily high order term, which fills the gap in the computational shell theory. Finally, numerical results for the saddle shell and cylindrical shell confirm the theoretical prediction.
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来源期刊
CiteScore
1.70
自引率
10.00%
发文量
59
审稿时长
6 months
期刊介绍: Covers modern applied mathematics in the fields of modeling, applied and stochastic analyses and numerical computations—on problems that arise in physical, biological, engineering, and financial applications. The journal publishes high-quality, original research articles, reviews, and expository papers.
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