On the stability of the Rayleigh-Ritz method for eigenvalues

被引：9

作者：

Gallistl, D. ^{[1
]}

Huber, P. ^{[2
]}

Peterseim, D. ^{[3
]}

机构：

[1] Karlsruher Inst Technol, Inst Angew & Numer Math, D-76128 Karlsruhe, Germany

[2] Univ Bonn, Inst Numer Simulat, Endenicher Allee 60, D-53115 Bonn, Germany

[3] Univ Augsburg, Inst Math, Univ Str 14, D-86159 Augsburg, Germany

来源：

NUMERISCHE MATHEMATIK | 2017年 / 137卷 / 02期

关键词：

ISOGEOMETRIC ANALYSIS; WAVE-PROPAGATION; FINITE-ELEMENTS; NURBS; APPROXIMATIONS;

D O I：

10.1007/s00211-017-0876-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper studies global stability properties of the Rayleigh-Ritz approximation of eigenvalues of the Laplace operator. The focus lies on the ratios of the kth numerical eigenvalue and the kth exact eigenvalue . 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.

引用

页码：339 / 351

页数：13

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