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Three methods for two‐sided bounds of eigenvalues—A comparison
Author(s) -
Vejchodský Tomáš
Publication year - 2018
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22251
Subject(s) - mathematics , eigenvalues and eigenvectors , generality , finite element method , estimator , complementarity (molecular biology) , order (exchange) , statistics , psychology , physics , genetics , finance , quantum mechanics , biology , economics , psychotherapist , thermodynamics
We compare three finite element‐based methods designed for two‐sided bounds of eigenvalues of symmetric elliptic second order operators. The first method is known as the Lehmann–Goerisch method. The second method is based on Crouzeix–Raviart nonconforming finite element method. The third one is a combination of generalized Weinstein and Kato bounds with complementarity‐based estimators. We concisely describe these methods and use them to solve three numerical examples. We compare their accuracy, computational performance, and generality in both the lowest and higher order case.