非自相交特征值问题的缺陷特征值 FE 近似的后验误差估计值

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Numerical Analysis Pub Date : 2024-11-04 DOI:10.1137/23m162065x

Yidu Yang, Shixi Wang, Hai Bi

{"title":"非自相交特征值问题的缺陷特征值 FE 近似的后验误差估计值","authors":"Yidu Yang, Shixi Wang, Hai Bi","doi":"10.1137/23m162065x","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 62, Issue 6, Page 2419-2438, December 2024. <br/> Abstract. In this paper, we study the a posteriori error estimates of the FEM for defective eigenvalues of non-self-adjoint eigenvalue problems. Using the spectral approximation theory, we establish the abstract a posteriori error formulas for the weighted average of approximate eigenvalues and approximate eigenspace. We then apply the formulas to the defective eigenvalues of elliptic interface problem, derive the a posteriori error estimators, and analyze their reliability and effectiveness. We also provide numerical examples to confirm our theoretical findings.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"8 1","pages":""},"PeriodicalIF":2.8000,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The A Posteriori Error Estimates of the FE Approximation of Defective Eigenvalues for Non-Self-Adjoint Eigenvalue Problems\",\"authors\":\"Yidu Yang, Shixi Wang, Hai Bi\",\"doi\":\"10.1137/23m162065x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"SIAM Journal on Numerical Analysis, Volume 62, Issue 6, Page 2419-2438, December 2024. <br/> Abstract. In this paper, we study the a posteriori error estimates of the FEM for defective eigenvalues of non-self-adjoint eigenvalue problems. Using the spectral approximation theory, we establish the abstract a posteriori error formulas for the weighted average of approximate eigenvalues and approximate eigenspace. We then apply the formulas to the defective eigenvalues of elliptic interface problem, derive the a posteriori error estimators, and analyze their reliability and effectiveness. We also provide numerical examples to confirm our theoretical findings.\",\"PeriodicalId\":49527,\"journal\":{\"name\":\"SIAM Journal on Numerical Analysis\",\"volume\":\"8 1\",\"pages\":\"\"},\"PeriodicalIF\":2.8000,\"publicationDate\":\"2024-11-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"SIAM Journal on Numerical Analysis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1137/23m162065x\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Numerical Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/23m162065x","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

摘要

SIAM 数值分析期刊》，第 62 卷，第 6 期，第 2419-2438 页，2024 年 12 月。摘要本文研究了非自相交特征值问题的缺陷特征值有限元的后验误差估计。利用谱近似理论，我们建立了近似特征值加权平均和近似特征空间的抽象后验误差公式。然后，我们将这些公式应用于椭圆界面问题的缺陷特征值，推导出后验误差估计值，并分析其可靠性和有效性。我们还提供了数值实例来证实我们的理论发现。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

The A Posteriori Error Estimates of the FE Approximation of Defective Eigenvalues for Non-Self-Adjoint Eigenvalue Problems

SIAM Journal on Numerical Analysis, Volume 62, Issue 6, Page 2419-2438, December 2024.
Abstract. In this paper, we study the a posteriori error estimates of the FEM for defective eigenvalues of non-self-adjoint eigenvalue problems. Using the spectral approximation theory, we establish the abstract a posteriori error formulas for the weighted average of approximate eigenvalues and approximate eigenspace. We then apply the formulas to the defective eigenvalues of elliptic interface problem, derive the a posteriori error estimators, and analyze their reliability and effectiveness. We also provide numerical examples to confirm our theoretical findings.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

SIAM Journal on Numerical Analysis 数学-应用数学

CiteScore

4.80

自引率

6.90%

发文量

110

审稿时长

4-8 weeks

期刊介绍： SIAM Journal on Numerical Analysis (SINUM) contains research articles on the development and analysis of numerical methods. Topics include the rigorous study of convergence of algorithms, their accuracy, their stability, and their computational complexity. Also included are results in mathematical analysis that contribute to algorithm analysis, and computational results that demonstrate algorithm behavior and applicability.