@article{GaHuPe17,
author = {Gallistl, D. and Huber, P. and Peterseim, D.},
title = {On the stability of the {R}ayleigh--{R}itz method for eigenvalues},
journal = {Numerische Mathematik},
year = {2017},
volume = {137},
pages = {339--351},
number = {2},
month = {Oct},
abstract = {This paper studies global stability properties of the Rayleigh--Ritz
approximation of eigenvalues of the Laplace operator. The focus lies
on the ratios $\hat{\lambda}_k/\lambda_k$ of the $k$th numerical
eigenvalue $\hat{\lambda}_k$ and the $k$th exact eigenvalue $\lambda_k$.
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.},
day = {01},
doi = {10.1007/s00211-017-0876-8},
issn = {0945-3245},
keywords = {isogeometric analysis, eigenvalues, inverse inequality},
url = {https://doi.org/10.1007/s00211-017-0876-8}
}