{"title":"Flexible Ultra-convergence Structures for the Finite Volume Element Method","authors":"Xiang Wang, Yuqing Zhang, Zhimin Zhang","doi":"10.1007/s10915-024-02654-7","DOIUrl":null,"url":null,"abstract":"<p>We introduce a novel class of ultra-convergent structures for the Finite Volume Element (FVE) method. These structures are characterized by asymmetric and optional superconvergent points. We establish a crucial relationship between ultra-convergence properties and the orthogonality condition. Remarkably, within this framework, certain FVE schemes achieve simultaneous superconvergence of both derivatives and function values at designated points, as demonstrated in Example 2. This is a phenomenon rarely observed in other numerical methods. Theoretical validation of these findings is provided through the proposed Generalized M-Decomposition (GMD). Numerical experiments effectively substantiate our results.</p>","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":"1 1","pages":""},"PeriodicalIF":2.8000,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Scientific Computing","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10915-024-02654-7","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
We introduce a novel class of ultra-convergent structures for the Finite Volume Element (FVE) method. These structures are characterized by asymmetric and optional superconvergent points. We establish a crucial relationship between ultra-convergence properties and the orthogonality condition. Remarkably, within this framework, certain FVE schemes achieve simultaneous superconvergence of both derivatives and function values at designated points, as demonstrated in Example 2. This is a phenomenon rarely observed in other numerical methods. Theoretical validation of these findings is provided through the proposed Generalized M-Decomposition (GMD). Numerical experiments effectively substantiate our results.
期刊介绍:
Journal of Scientific Computing is an international interdisciplinary forum for the publication of papers on state-of-the-art developments in scientific computing and its applications in science and engineering.
The journal publishes high-quality, peer-reviewed original papers, review papers and short communications on scientific computing.