{"title":"Optimal maximum norm estimates of virtual element methods for elliptic problem in three dimensions","authors":"Wenming He , Ren Zhao","doi":"10.1016/j.camwa.2025.08.011","DOIUrl":null,"url":null,"abstract":"<div><div>In this article, we derive the optimal maximum norm estimates for virtual element methods for elliptic problems in three dimensions under suitable local smoothness assumption of the solution. Finally, numerical examples are used to investigate our main results on tetrahedral and polyhedral meshes.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"197 ","pages":"Pages 167-182"},"PeriodicalIF":2.5000,"publicationDate":"2025-08-26","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/S0898122125003384","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
Abstract
In this article, we derive the optimal maximum norm estimates for virtual element methods for elliptic problems in three dimensions under suitable local smoothness assumption of the solution. Finally, numerical examples are used to investigate our main results on tetrahedral and polyhedral meshes.
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).