虚拟元素法的内部估计

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Numerische Mathematik Pub Date : 2024-05-09 DOI:10.1007/s00211-024-01408-9

Silvia Bertoluzza, Micol Pennacchio, Daniele Prada

{"title":"虚拟元素法的内部估计","authors":"Silvia Bertoluzza, Micol Pennacchio, Daniele Prada","doi":"10.1007/s00211-024-01408-9","DOIUrl":null,"url":null,"abstract":"We analyze the local accuracy of the virtual element method. More precisely, we prove an error bound similar to the one holding for the finite element method, namely, that the local \\(H^1\\) error in a interior subdomain is bounded by a term behaving like the best approximation allowed by the local smoothness of the solution in a larger interior subdomain plus the global error measured in a negative norm.\n","PeriodicalId":49733,"journal":{"name":"Numerische Mathematik","volume":null,"pages":null},"PeriodicalIF":2.1000,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Interior estimates for the virtual element method\",\"authors\":\"Silvia Bertoluzza, Micol Pennacchio, Daniele Prada\",\"doi\":\"10.1007/s00211-024-01408-9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We analyze the local accuracy of the virtual element method. More precisely, we prove an error bound similar to the one holding for the finite element method, namely, that the local \\\\(H^1\\\\) error in a interior subdomain is bounded by a term behaving like the best approximation allowed by the local smoothness of the solution in a larger interior subdomain plus the global error measured in a negative norm.\\n\",\"PeriodicalId\":49733,\"journal\":{\"name\":\"Numerische Mathematik\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.1000,\"publicationDate\":\"2024-05-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Numerische Mathematik\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00211-024-01408-9\",\"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":"Numerische Mathematik","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00211-024-01408-9","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

我们分析了虚拟元素方法的局部精度。更准确地说，我们证明了一个与有限元法类似的误差约束，即内部子域的局部误差由一个项约束，这个项的行为类似于较大内部子域中局部平滑解所允许的最佳近似值加上以负规范测量的全局误差。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Interior estimates for the virtual element method

查看原文本刊更多论文

Interior estimates for the virtual element method

We analyze the local accuracy of the virtual element method. More precisely, we prove an error bound similar to the one holding for the finite element method, namely, that the local \(H^1\) error in a interior subdomain is bounded by a term behaving like the best approximation allowed by the local smoothness of the solution in a larger interior subdomain plus the global error measured in a negative norm.

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

Numerische Mathematik 数学-应用数学

CiteScore

4.10

自引率

4.80%

发文量

审稿时长

6-12 weeks

期刊介绍： Numerische Mathematik publishes papers of the very highest quality presenting significantly new and important developments in all areas of Numerical Analysis. "Numerical Analysis" is here understood in its most general sense, as that part of Mathematics that covers: 1. The conception and mathematical analysis of efficient numerical schemes actually used on computers (the "core" of Numerical Analysis) 2. Optimization and Control Theory 3. Mathematical Modeling 4. The mathematical aspects of Scientific Computing