Convergence Rate and Quasi-Optimal Complexity of Adaptive Finite Element Computations for Multiple Eigenvalues

2012/10/06 by Xiaoying Dai, Dai, Xiaoying, Lianhua He +3 · 6 citations
Computer Science · Engineering · #65F15 #65N15 #65N25 #65N30 #65N50 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1210.1846

openalex publication_date 2012/10/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study an adaptive finite element method for multiple eigenvalue problems of a class of second order elliptic equations. By using some eigenspace approximation technology and its crucial property which is also presented in this paper, we extend the results in \citedai-xu-zhou08 to multiple eigenvalue problems, we obtain both convergence rate and quasi-optimal complexity of the adaptive finite element eigenvalue approximation.

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• The discontinuous Galerkin method for the Oseen eigenvalue problem
• Local Multilevel Preconditioned Jacobi-Davidson Method for Elliptic Eigenvalue Problems on Adaptive Meshes
• Pointwise A Posteriori Error Estimators for Multiple and Clustered Eigenvalue Computations
• An orthogonality-preserving approach for eigenvalue problems
• Convergence of the adaptive finite element discretization based parallel orbital-updating method for eigenvalue problems

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