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Computable upper and lower bounds on eigenfrequencies

Li Wang 1 Ludovic Chamoin 2, 3 Pierre Ladevèze 2 Hongzhi Zhong 1
3 MATHERIALS - MATHematics for MatERIALS
CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique, Inria Paris-Rocquencourt, ENPC - École des Ponts ParisTech
Abstract : This paper is a revisit of the work [Ladevèze and Pelle, Int. J. Numer. Methods Engrg. 28 (1989)] where the goal here is to acquire guaranteed, accurate and computable bounds of eigenfrequencies through post-processing of conventional finite element results. To this end, a new theoretical quotient is introduced and thereafter, a practical way to deal with the new quotient is developed where the constitutive relation error estimation featured with guaranteed bounding property acts as a key role. Academic numerical examples are performed to check the accuracy of the bounds.
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https://hal.archives-ouvertes.fr/hal-01241742
Contributor : Ludovic Chamoin <>
Submitted on : Thursday, December 10, 2015 - 10:58:47 PM
Last modification on : Friday, May 24, 2019 - 5:24:33 PM

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Li Wang, Ludovic Chamoin, Pierre Ladevèze, Hongzhi Zhong. Computable upper and lower bounds on eigenfrequencies. Computer Methods in Applied Mechanics and Engineering, Elsevier, 2016, 302, pp.27-43. ⟨10.1016/j.cma.2016.01.002⟩. ⟨hal-01241742⟩

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