{"title":"On the number of reliable finite-element eigenmodes","authors":"D. Givoli","doi":"10.1002/CNM.1088","DOIUrl":null,"url":null,"abstract":"The finite-element (FE) approximation of linear elliptic eigenvalue problems is considered. An analysis based on a number of known estimates leads to the simple formula M=r0ed/(2p)N relating the total number of degrees of freedom N, the maximum relative error level e desired for the eigenvalues, and the number of ‘reliable’ modes M. (Here d is the spatial dimension and p is the polynomial degree of the FE space.) Moreover, a rough estimate for the numerical value of the constant r0 for a given application is found. This result supports a well-known rule of thumb. Copyright © 2008 John Wiley & Sons, Ltd.","PeriodicalId":51245,"journal":{"name":"Communications in Numerical Methods in Engineering","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2008-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/CNM.1088","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Numerical Methods in Engineering","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1002/CNM.1088","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 4
可靠有限元本征模态的数目
研究线性椭圆型特征值问题的有限元逼近。基于一些已知估计的分析得出了一个简单的公式M= red /(2p)N，它与总自由度N、特征值所需的最大相对误差水平e和“可靠”模式M的数量有关(这里d是空间维度，p是FE空间的多项式度)。此外，还找到了给定应用中常数r0数值的粗略估计。这个结果支持一个众所周知的经验法则。版权所有©2008 John Wiley & Sons, Ltd
本文章由计算机程序翻译，如有差异，请以英文原文为准。
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