{"title":"An implementation detail about the scaling of monomial bases in polytopal finite element methods","authors":"","doi":"10.1016/j.aml.2024.109281","DOIUrl":null,"url":null,"abstract":"<div><p>The usual definition of scaled monomials found in polytopal finite elements literature leads to elemental matrices with an unnecessarily high condition number. A trivial but apparently overlooked rescaling significantly improves the situation. The extent of the improvement is demonstrated numerically.</p></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":2.9000,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S089396592400301X/pdfft?md5=b6d87c88bcb4ca6fa1e7e4b5018156d8&pid=1-s2.0-S089396592400301X-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics Letters","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S089396592400301X","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
The usual definition of scaled monomials found in polytopal finite elements literature leads to elemental matrices with an unnecessarily high condition number. A trivial but apparently overlooked rescaling significantly improves the situation. The extent of the improvement is demonstrated numerically.
期刊介绍：
The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.
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