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[1] D. Gallistl, P. Huber, and D. Peterseim. On the stability of the Rayleigh-Ritz method for eigenvalues. Numerische Mathematik, 137(2):339-351, Oct 2017.
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This paper studies global stability properties of the Rayleigh-Ritz approximation of eigenvalues of the Laplace operator. The focus lies on the ratios \lambdakk of the kth numerical eigenvalue \lambdak 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.

Keywords: isogeometric analysis, eigenvalues, inverse inequality