{"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":"<p>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 <span>\\(H^1\\)</span> 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</p>","PeriodicalId":49733,"journal":{"name":"Numerische Mathematik","volume":"32 1","pages":""},"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\":\"<p>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 <span>\\\\(H^1\\\\)</span> 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</p>\",\"PeriodicalId\":49733,\"journal\":{\"name\":\"Numerische Mathematik\",\"volume\":\"32 1\",\"pages\":\"\"},\"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}
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.
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
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