{"title":"Unfitted mixed finite element methods for elliptic interface problems","authors":"Najwa Alshehri, Daniele Boffi, Lucia Gastaldi","doi":"10.1002/num.23063","DOIUrl":null,"url":null,"abstract":"Abstract In this article, new unfitted mixed finite elements are presented for elliptic interface problems with jump coefficients. Our model is based on a fictitious domain formulation with distributed Lagrange multiplier. The relevance of our investigations is better seen when applied to the framework of fluid‐structure interaction problems. Two finite element schemes with piecewise constant Lagrange multiplier are proposed and their stability is proved theoretically. Numerical results compare the performance of those elements, confirming the theoretical proofs and verifying that the schemes converge with optimal rates.","PeriodicalId":19443,"journal":{"name":"Numerical Methods for Partial Differential Equations","volume":"22 1","pages":"0"},"PeriodicalIF":2.1000,"publicationDate":"2023-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Numerical Methods for Partial Differential Equations","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1002/num.23063","RegionNum":3,"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: 1
Abstract
Abstract In this article, new unfitted mixed finite elements are presented for elliptic interface problems with jump coefficients. Our model is based on a fictitious domain formulation with distributed Lagrange multiplier. The relevance of our investigations is better seen when applied to the framework of fluid‐structure interaction problems. Two finite element schemes with piecewise constant Lagrange multiplier are proposed and their stability is proved theoretically. Numerical results compare the performance of those elements, confirming the theoretical proofs and verifying that the schemes converge with optimal rates.
IF 6.3 4区 医学Systematic ReviewsPub Date : 2022-10-26DOI: 10.1186/s13643-022-02099-9
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IF 0 medRxiv - OncologyPub Date : 2024-05-31DOI: 10.1101/2024.05.29.24308154
Alexandria Bennett, Nicole Shaver, Niyati Vyas, Faris Almoli, Robert Pap, Andrea Douglas, Taddele Kibret, Becky Skidmore, Martin Yaffe, Anna Wilkinson, Jean M. Seely, Julian Little, David Moher
期刊介绍:
An international journal that aims to cover research into the development and analysis of new methods for the numerical solution of partial differential equations, it is intended that it be readily readable by and directed to a broad spectrum of researchers into numerical methods for partial differential equations throughout science and engineering. The numerical methods and techniques themselves are emphasized rather than the specific applications. The Journal seeks to be interdisciplinary, while retaining the common thread of applied numerical analysis.