On the stability of the Rayleigh-Ritz method for eigenvalues
On the stability of the Rayleigh-Ritz method for eigenvalues
View/Date of Publication
05.01.2017Publisher
Institut für Numerische Simulation (INS)Publisher Location
BonnMetadata
Show full item record
Citable Link (Handle URI) 
https://hdl.handle.net/20.500.11811/11905
Abstract
This paper studies global stability properties of the Rayleigh-Ritz approximation of eigenvalues of the Laplace operator. The focus lies on the ratios ^λk/λk of the kth numerical eigenvalue ^λk and the kth exact eigenvalue λk. In the context of classical finite elements, the maximal ratio blows up with the polynomial degree. For B-splines of maximum smoothness, the ratios are uniformly bounded with respect to the degree except for a few instable numerical eigenvalues which are related to the presence of essential boundary conditions. These phenomena are linked to the inverse inequalities in the respective approximation spaces.
Classification (DDC)
510 Mathematik 518 Numerische AnalysisFirst Publication
https://ins.uni-bonn.de/publication/preprintsRelated Publications
https://doi.org/10.1007/s00211-017-0876-8Part of Series
INS Preprints ; 1527Gallistl, Dietmar; Patrick, Huber; Peterseim, Daniel: On the stability of the Rayleigh-Ritz method for eigenvalues. In: INS Preprints, 1527.
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11905
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11905
@unpublished{handle:20.500.11811/11905,
author = {{Dietmar Gallistl} and {Huber Patrick} and {Daniel Peterseim}},
title = {On the stability of the Rayleigh-Ritz method for eigenvalues},
publisher = {Institut für Numerische Simulation (INS)},
year = 2017,
month = jan,
INS Preprints},
volume = 1527,
note = {This paper studies global stability properties of the Rayleigh-Ritz approximation of eigenvalues of the Laplace operator. The focus lies on the ratios ^λk/λk of the kth numerical eigenvalue ^λk and the kth exact eigenvalue λk. In the context of classical finite elements, the maximal ratio blows up with the polynomial degree. For B-splines of maximum smoothness, the ratios are uniformly bounded with respect to the degree except for a few instable numerical eigenvalues which are related to the presence of essential boundary conditions. These phenomena are linked to the inverse inequalities in the respective approximation spaces.},
url = {https://hdl.handle.net/20.500.11811/11905}
}
author = {{Dietmar Gallistl} and {Huber Patrick} and {Daniel Peterseim}},
title = {On the stability of the Rayleigh-Ritz method for eigenvalues},
publisher = {Institut für Numerische Simulation (INS)},
year = 2017,
month = jan,
INS Preprints},
volume = 1527,
note = {This paper studies global stability properties of the Rayleigh-Ritz approximation of eigenvalues of the Laplace operator. The focus lies on the ratios ^λk/λk of the kth numerical eigenvalue ^λk and the kth exact eigenvalue λk. In the context of classical finite elements, the maximal ratio blows up with the polynomial degree. For B-splines of maximum smoothness, the ratios are uniformly bounded with respect to the degree except for a few instable numerical eigenvalues which are related to the presence of essential boundary conditions. These phenomena are linked to the inverse inequalities in the respective approximation spaces.},
url = {https://hdl.handle.net/20.500.11811/11905}
}
The following license files are associated with this item:
