{"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}
引用次数: 0
Abstract
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.
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.
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