@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}
}