On the spectrum of the finite element approximation of a three field formulation for linear elasticity

Linda Alzaben , Fleurianne Bertrand , Daniele Boffi
{"title":"On the spectrum of the finite element approximation of a three field formulation for linear elasticity","authors":"Linda Alzaben ,&nbsp;Fleurianne Bertrand ,&nbsp;Daniele Boffi","doi":"10.1016/j.exco.2022.100076","DOIUrl":null,"url":null,"abstract":"<div><p>We continue the investigation on the spectrum of operators arising from the discretization of partial differential equations. In this paper we consider a three field formulation recently introduced for the finite element least-squares approximation of linear elasticity. We discuss in particular the distribution of the discrete eigenvalues in the complex plane and how they approximate the positive real eigenvalues of the continuous problem. The dependence of the spectrum on the Lamé parameters is considered as well and its behavior when approaching the incompressible limit.</p></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"2 ","pages":"Article 100076"},"PeriodicalIF":0.0000,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2666657X22000155/pdfft?md5=fb9d2e5112e427f0af0000cd842cd071&pid=1-s2.0-S2666657X22000155-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Examples and Counterexamples","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2666657X22000155","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

Abstract

We continue the investigation on the spectrum of operators arising from the discretization of partial differential equations. In this paper we consider a three field formulation recently introduced for the finite element least-squares approximation of linear elasticity. We discuss in particular the distribution of the discrete eigenvalues in the complex plane and how they approximate the positive real eigenvalues of the continuous problem. The dependence of the spectrum on the Lamé parameters is considered as well and its behavior when approaching the incompressible limit.

查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
线性弹性三场公式的有限元近似谱
我们继续研究由偏微分方程离散化引起的算子谱。在本文中,我们考虑了最近引入的线性弹性有限元最小二乘近似的三场公式。我们特别讨论了离散本征值在复平面上的分布,以及它们如何逼近连续问题的正实本征值。还考虑了谱对Lamé参数的依赖性及其在接近不可压缩极限时的行为。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
CiteScore
0.80
自引率
0.00%
发文量
0
期刊最新文献
Automation of image processing through ML algorithms of GRASS GIS using embedded Scikit-Learn library of Python Counterexamples for your calculus course Hölder’s inequality for shifted quantum integral operator Solving change of basis from Bernstein to Chebyshev polynomials Asymptotic behavior of the empirical checkerboard copula process for binary data: An educational presentation
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1