{"title":"Exact integration for singular Zienkiewicz and Guzmán–Neilan finite elements with implementation","authors":"Lars Diening , Johannes Storn , Tabea Tscherpel","doi":"10.1016/j.camwa.2025.04.019","DOIUrl":null,"url":null,"abstract":"<div><div>We develop a recursive integration formula for a class of rational polynomials in 2D. Based on this, we present implementations of finite elements that have rational basis functions. Specifically, we provide simple MATLAB implementations of the singular Zienkiewicz and the lowest-order Guzmán–Neilan finite element in 2D.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"191 ","pages":"Pages 60-85"},"PeriodicalIF":2.5000,"publicationDate":"2025-08-01","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/S0898122125001634","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2025/4/28 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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Abstract
We develop a recursive integration formula for a class of rational polynomials in 2D. Based on this, we present implementations of finite elements that have rational basis functions. Specifically, we provide simple MATLAB implementations of the singular Zienkiewicz and the lowest-order Guzmán–Neilan finite element in 2D.
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).
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