{"title":"斯托克斯特征值的下限和上限","authors":"Yifan Yue, Hongtao Chen, Shuo Zhang","doi":"10.1007/s10092-024-00598-w","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we study the lower and upper bounds for Stokes eigenvalues by finite element schemes. For the schemes studied here, roughly speaking, the loss of the local approximation property of the discrete <b>velocity</b> and <b>pressure</b> spaces may lead to different computed bounds of the eigenvalues. Formally theoretical analysis is constructed based on certain mathematical hypotheses, and numerical experiments are given to illustrate the validity of the theory.</p>","PeriodicalId":9522,"journal":{"name":"Calcolo","volume":"25 1","pages":""},"PeriodicalIF":1.4000,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Lower and upper bounds for stokes eigenvalues\",\"authors\":\"Yifan Yue, Hongtao Chen, Shuo Zhang\",\"doi\":\"10.1007/s10092-024-00598-w\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this paper, we study the lower and upper bounds for Stokes eigenvalues by finite element schemes. For the schemes studied here, roughly speaking, the loss of the local approximation property of the discrete <b>velocity</b> and <b>pressure</b> spaces may lead to different computed bounds of the eigenvalues. Formally theoretical analysis is constructed based on certain mathematical hypotheses, and numerical experiments are given to illustrate the validity of the theory.</p>\",\"PeriodicalId\":9522,\"journal\":{\"name\":\"Calcolo\",\"volume\":\"25 1\",\"pages\":\"\"},\"PeriodicalIF\":1.4000,\"publicationDate\":\"2024-07-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Calcolo\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s10092-024-00598-w\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Calcolo","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10092-024-00598-w","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
In this paper, we study the lower and upper bounds for Stokes eigenvalues by finite element schemes. For the schemes studied here, roughly speaking, the loss of the local approximation property of the discrete velocity and pressure spaces may lead to different computed bounds of the eigenvalues. Formally theoretical analysis is constructed based on certain mathematical hypotheses, and numerical experiments are given to illustrate the validity of the theory.
期刊介绍：
Calcolo is a quarterly of the Italian National Research Council, under the direction of the Institute for Informatics and Telematics in Pisa. Calcolo publishes original contributions in English on Numerical Analysis and its Applications, and on the Theory of Computation.
The main focus of the journal is on Numerical Linear Algebra, Approximation Theory and its Applications, Numerical Solution of Differential and Integral Equations, Computational Complexity, Algorithmics, Mathematical Aspects of Computer Science, Optimization Theory.
Expository papers will also appear from time to time as an introduction to emerging topics in one of the above mentioned fields. There will be a "Report" section, with abstracts of PhD Theses, news and reports from conferences and book reviews. All submissions will be carefully refereed.
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