Nonconforming finite element method for a 4th-order history-dependent hemivariational inequality

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-03-11 DOI:10.1016/j.cnsns.2025.108750

Jiali Qiu , Min Ling , Fei Wang , Bangmin Wu

引用次数: 0

Abstract

This paper explores the analysis and numerical solution of a fourth-order history-dependent hemivariational inequality. The variational formulation is derived from a model describing an elastic plate in contact with a reactive obstacle, where the contact condition involves both the subdifferential of a nonconvex, nonsmooth function and a Volterra-type integral term. We discretize the continuous formulation using the left rectangle rule to handle the history-dependent operator, along with a Morley finite element method for spatial discretization. A priori error estimates for the fully discrete scheme are established, demonstrating optimal convergence. Numerical examples are provided to verify the theoretical findings.

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一类四阶历史相关半分不等式的非协调有限元法

本文研究了一类四阶历史相关半变不等式的分析与数值解。变分公式是从描述弹性板与反应性障碍物接触的模型中导出的，其中接触条件涉及非凸非光滑函数的次微分和volterra型积分项。我们使用左矩形规则来处理历史相关算子来离散连续公式，并使用Morley有限元法进行空间离散。建立了完全离散格式的先验误差估计，证明了最优收敛性。数值算例验证了理论结果。

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

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.