接触问题虚元法的先验误差分析

Fixed Point Theory and Applications Pub Date : 2022-04-01 DOI:10.1186/s13663-022-00720-z

Wang, Fei, Reddy, B. Daya

{"title":"接触问题虚元法的先验误差分析","authors":"Wang, Fei, Reddy, B. Daya","doi":"10.1186/s13663-022-00720-z","DOIUrl":null,"url":null,"abstract":"As an extension of the finite element method, the virtual element method (VEM) can handle very general polygonal meshes, making it very suitable for non-matching meshes. In (Wriggers et al. in Comput. Mech. 58:1039–1050, 2016), the lowest-order virtual element method was applied to solve the contact problem of two elastic bodies on non-matching meshes. The numerical experiments showed the robustness and accuracy of the virtual element scheme. In this paper, we establish a priori error estimate of the virtual element method for the contact problem and prove that the lowest-order VEM achieves linear convergence order, which is optimal.","PeriodicalId":12293,"journal":{"name":"Fixed Point Theory and Applications","volume":"184 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"A priori error analysis of virtual element method for contact problem\",\"authors\":\"Wang, Fei, Reddy, B. Daya\",\"doi\":\"10.1186/s13663-022-00720-z\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"As an extension of the finite element method, the virtual element method (VEM) can handle very general polygonal meshes, making it very suitable for non-matching meshes. In (Wriggers et al. in Comput. Mech. 58:1039–1050, 2016), the lowest-order virtual element method was applied to solve the contact problem of two elastic bodies on non-matching meshes. The numerical experiments showed the robustness and accuracy of the virtual element scheme. In this paper, we establish a priori error estimate of the virtual element method for the contact problem and prove that the lowest-order VEM achieves linear convergence order, which is optimal.\",\"PeriodicalId\":12293,\"journal\":{\"name\":\"Fixed Point Theory and Applications\",\"volume\":\"184 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-04-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Fixed Point Theory and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1186/s13663-022-00720-z\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fixed Point Theory and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1186/s13663-022-00720-z","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 3

摘要

虚元法作为有限元法的一种扩展，可以处理非常一般的多边形网格，使其非常适用于非匹配网格。在《Wriggers et al. In Comput》中。机械学报(58:1039-1050,2016)，采用最低阶虚元法求解两个弹性体在不匹配网格上的接触问题。数值实验证明了该方法的鲁棒性和准确性。本文建立了接触问题虚元法的先验误差估计，并证明了最低阶VEM达到线性收敛阶，是最优的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

A priori error analysis of virtual element method for contact problem

As an extension of the finite element method, the virtual element method (VEM) can handle very general polygonal meshes, making it very suitable for non-matching meshes. In (Wriggers et al. in Comput. Mech. 58:1039–1050, 2016), the lowest-order virtual element method was applied to solve the contact problem of two elastic bodies on non-matching meshes. The numerical experiments showed the robustness and accuracy of the virtual element scheme. In this paper, we establish a priori error estimate of the virtual element method for the contact problem and prove that the lowest-order VEM achieves linear convergence order, which is optimal.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Fixed Point Theory and Applications MATHEMATICS, APPLIED-MATHEMATICS

自引率

0.00%

发文量

期刊介绍： In a wide range of mathematical, computational, economical, modeling and engineering problems, the existence of a solution to a theoretical or real world problem is equivalent to the existence of a fixed point for a suitable map or operator. Fixed points are therefore of paramount importance in many areas of mathematics, sciences and engineering. The theory itself is a beautiful mixture of analysis (pure and applied), topology and geometry. Over the last 60 years or so, the theory of fixed points has been revealed as a very powerful and important tool in the study of nonlinear phenomena. In particular, fixed point techniques have been applied in such diverse fields as biology, chemistry, physics, engineering, game theory and economics. In numerous cases finding the exact solution is not possible; hence it is necessary to develop appropriate algorithms to approximate the requested result. This is strongly related to control and optimization problems arising in the different sciences and in engineering problems. Many situations in the study of nonlinear equations, calculus of variations, partial differential equations, optimal control and inverse problems can be formulated in terms of fixed point problems or optimization.