Semidiscrete numerical approximation for dynamic hemivariational inequalities with history-dependent operators

IF 1.1 4区数学 Q2 MATHEMATICS, APPLIED Applicable Analysis Pub Date : 2023-10-19 DOI:10.1080/00036811.2023.2271031

Yujie Li, Xiaoliang Cheng, Hailing Xuan

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Abstract

AbstractIn this paper, we are concerned with a class of second-order hemivariational inequalities involving history-dependent operators. For the problem, we first derive a semidiscrete scheme by implicit Euler formula and prove its unique solvability. The existence and uniqueness of a solution to the inequality problem is given by Rothe method. As the core part of the paper, we propose a two-step semidiscrete approximation for the problem, provide its unique solvability and obtain its second-order error estimates. The two-step scheme is more accurate than the standard implicit Euler scheme. Finally, we apply the results to a dynamic frictionless contact problem with long memory.Keywords: Hemivariational inequalitycontact problemhistory-dependent operatorerror estimatesMathematic Subject classifications: 65M1565N2274H15 Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThe authors would like to thank the anonymous reviewers for their valuable comments and suggestions. This work was supported by the European Unions Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie Grand Agreement No. 823731 CONMECH.

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具有历史相关算子的动态半分不等式的半离散数值逼近

摘要本文研究了一类包含历史相关算子的二阶半变不等式。对于该问题，首先利用隐式欧拉公式导出了一个半离散格式，并证明了它的唯一可解性。用Rothe方法给出了不等式问题解的存在唯一性。作为论文的核心部分，我们提出了该问题的两步半离散逼近，给出了该问题的唯一可解性，并得到了该问题的二阶误差估计。两步格式比标准隐式欧拉格式更精确。最后，我们将结果应用于具有长记忆的动态无摩擦接触问题。关键词:半分不等式接触问题历史相关算子误差估计数学学科分类:65M1565N2274H15披露声明作者未报告潜在利益冲突。作者感谢匿名审稿人提供的宝贵意见和建议。这项工作得到了欧盟地平线2020研究与创新计划的支持，该计划由玛丽·斯克洛多夫斯卡-居里大协议823731 CONMECH资助。

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来源期刊

Applicable Analysis 数学-应用数学

CiteScore

2.60

自引率

9.10%

发文量

175

审稿时长

2 months

期刊介绍： Applicable Analysis is concerned primarily with analysis that has application to scientific and engineering problems. Papers should indicate clearly an application of the mathematics involved. On the other hand, papers that are primarily concerned with modeling rather than analysis are outside the scope of the journal General areas of analysis that are welcomed contain the areas of differential equations, with emphasis on PDEs, and integral equations, nonlinear analysis, applied functional analysis, theoretical numerical analysis and approximation theory. Areas of application, for instance, include the use of homogenization theory for electromagnetic phenomena, acoustic vibrations and other problems with multiple space and time scales, inverse problems for medical imaging and geophysics, variational methods for moving boundary problems, convex analysis for theoretical mechanics and analytical methods for spatial bio-mathematical models.