用于 von Kármán 方程的莫雷型虚拟元素法

IF 1.7 3区数学 Q2 MATHEMATICS, APPLIED

Advances in Computational Mathematics Pub Date : 2024-08-22 DOI:10.1007/s10444-024-10158-z

Devika Shylaja, Sarvesh Kumar

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引用次数: 0

摘要

本文分析了用于近似描述极薄弹性板弯曲的 von Kármán 方程正则解的非符合莫里型虚拟元素方法。讨论了非线性问题离散解的局部存在性和唯一性。在精确解的最小正则性假设下，建立了能量规范的先验误差估计。此外，还推导出了在\(H^1\) 和\(L^2\) 规范下的误差估计。讨论了使用牛顿法寻找离散解近似值的工作程序。给出了证明理论估计的数值结果。

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Morley type virtual element method for von Kármán equations

This paper analyses the nonconforming Morley type virtual element method to approximate a regular solution to the von Kármán equations that describes bending of very thin elastic plates. Local existence and uniqueness of a discrete solution to the non-linear problem is discussed. A priori error estimate in the energy norm is established under minimal regularity assumptions on the exact solution. Error estimates in piecewise \(H^1\) and \(L^2\) norms are also derived. A working procedure to find an approximation for the discrete solution using Newton’s method is discussed. Numerical results that justify theoretical estimates are presented.

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来源期刊

Advances in Computational Mathematics 数学-应用数学

CiteScore

3.00

自引率

5.90%

发文量

审稿时长

3 months

期刊介绍： Advances in Computational Mathematics publishes high quality, accessible and original articles at the forefront of computational and applied mathematics, with a clear potential for impact across the sciences. The journal emphasizes three core areas: approximation theory and computational geometry; numerical analysis, modelling and simulation; imaging, signal processing and data analysis. This journal welcomes papers that are accessible to a broad audience in the mathematical sciences and that show either an advance in computational methodology or a novel scientific application area, or both. Methods papers should rely on rigorous analysis and/or convincing numerical studies.