Three methods for two-sided bounds of eigenvalues-A comparison

0489414 - MÚ 2019 RIV US eng J - Journal Article
Vejchodský, Tomáš
Three methods for two-sided bounds of eigenvalues-A comparison.
Numerical Methods for Partial Differential Equations. Roč. 34, č. 4 (2018), s. 1188-1208. ISSN 0749-159X. E-ISSN 1098-2426
Institutional support: RVO:67985840
Keywords : complementarity * Crouzeix-Raviart elements * eigenvalue inclusions
OECD category: Pure mathematics
Impact factor: 1.633, year: 2018
https://onlinelibrary.wiley.com/doi/abs/10.1002/num.22251

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.
Permanent Link: http://hdl.handle.net/11104/0283835