非局部Kirchhoff型非线性问题的AFEM收敛性

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications Pub Date : 2025-04-28 DOI:10.1016/j.camwa.2025.04.020

Arnab Pal, Thirupathi Gudi

{"title":"非局部Kirchhoff型非线性问题的AFEM收敛性","authors":"Arnab Pal, Thirupathi Gudi","doi":"10.1016/j.camwa.2025.04.020","DOIUrl":null,"url":null,"abstract":"<div><div>In this article, plain convergence of an adaptive finite element method is shown for a non-local problem of Kirchhoff type under the same assumptions on the data as in the paper of T. Gudi (2012) <span><span>[21]</span></span>. Then by imposing some additional assumptions on the data, convergence and quasi-optimality of an AFEM is proved for the Kirchhoff type problem. The theoretical results are illustrated by some numerical experiments.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"189 ","pages":"Pages 176-193"},"PeriodicalIF":2.9000,"publicationDate":"2025-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Convergence of an AFEM for a non-local nonlinear problem of Kirchhoff type\",\"authors\":\"Arnab Pal, Thirupathi Gudi\",\"doi\":\"10.1016/j.camwa.2025.04.020\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>In this article, plain convergence of an adaptive finite element method is shown for a non-local problem of Kirchhoff type under the same assumptions on the data as in the paper of T. Gudi (2012) <span><span>[21]</span></span>. Then by imposing some additional assumptions on the data, convergence and quasi-optimality of an AFEM is proved for the Kirchhoff type problem. The theoretical results are illustrated by some numerical experiments.</div></div>\",\"PeriodicalId\":55218,\"journal\":{\"name\":\"Computers & Mathematics with Applications\",\"volume\":\"189 \",\"pages\":\"Pages 176-193\"},\"PeriodicalIF\":2.9000,\"publicationDate\":\"2025-04-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Computers & Mathematics with Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0898122125001737\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computers & Mathematics with Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0898122125001737","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

本文在与T. Gudi(2012)[21]的论文相同的数据假设下，展示了自适应有限元法对Kirchhoff型非局部问题的平实收敛性。然后通过在数据上附加一些假设，证明了求解Kirchhoff型问题的AFEM的收敛性和拟最优性。数值实验验证了理论结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Convergence of an AFEM for a non-local nonlinear problem of Kirchhoff type

In this article, plain convergence of an adaptive finite element method is shown for a non-local problem of Kirchhoff type under the same assumptions on the data as in the paper of T. Gudi (2012) [21]. Then by imposing some additional assumptions on the data, convergence and quasi-optimality of an AFEM is proved for the Kirchhoff type problem. The theoretical results are illustrated by some numerical experiments.

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

Computers & Mathematics with Applications 工程技术-计算机：跨学科应用

CiteScore

5.10

自引率

10.30%

发文量

396

审稿时长

9.9 weeks

期刊介绍： Computers & Mathematics with Applications provides a medium of exchange for those engaged in fields contributing to building successful simulations for science and engineering using Partial Differential Equations (PDEs).