FEM-implicit/explicit surface mesh discrete schemes for 2D-3C time-dependent shallow shell problem

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics Pub Date : 2025-07-05 DOI:10.1016/j.cam.2025.116878

Rongfang Wu , Xiaoqin Shen , Ying Liu , Yumin Cheng

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引用次数: 0

Abstract

In this work, we propose the finite element method (FEM) coupled implicit/explicit time difference schemes for the two-dimensional three-component (2D-3C) shallow shell surface equation, which features the second-order time variable and fourth-order space variable. Concretely, the higher-order spatial variable is discretized by employing a

C^{1}

-conforming element; meanwhile, the existence and uniqueness of semi-discrete solutions for the shallow shell model are analyzed using eigenvalues, and the optimal error estimate is obtained. Then, the time variable is discretized using the Newmark format. We prove that the space–time fully discretization scheme achieves first-order convergence when the parameter

γ \neq 0.5

. In addition, we adopt the leapfrog format to improve the convergence, which achieves second-order accuracy within small time steps. Finally, numerical experiments are conducted to validate the stability and efficiency of numerical algorithms.

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2D-3C时变浅壳问题的有限元隐/显曲面网格离散格式

本文提出了含二阶时间变量和四阶空间变量的二维三分量（2D-3C）浅壳面方程的有限元法（FEM）耦合隐/显时差格式。具体地说，高阶空间变量采用c1 -符合元离散化；同时，利用特征值分析了浅壳模型半离散解的存在唯一性，得到了最优误差估计。然后，使用Newmark格式对时间变量进行离散化。证明了当参数γ≠0.5时，时空完全离散化方案达到一阶收敛。此外，我们采用了跨越式格式来提高收敛性，在小时间步长内实现了二阶精度。最后，通过数值实验验证了数值算法的稳定性和有效性。

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

Journal of Computational and Applied Mathematics 数学-应用数学

CiteScore

5.40

自引率

4.20%

发文量

437

审稿时长

3.0 months

期刊介绍： The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest. The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.