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Two bracketing theorems characterizing the eigensolution for the h ‐version of the finite element method
Author(s) -
Meirovitch L.,
Silverberg L. M.
Publication year - 1983
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620191108
Subject(s) - bracketing (phenomenology) , mathematics , finite element method , discretization , interpolation (computer graphics) , eigenvalues and eigenvectors , mixed finite element method , element (criminal law) , mathematical analysis , calculus (dental) , computer science , physics , animation , medicine , philosophy , computer graphics (images) , dentistry , epistemology , quantum mechanics , political science , law , thermodynamics
Abstract This paper demonstrates that the classical inclusion principle is in general not valid for the h ‐version of the finite element method. Whereas the inclusion principle is valid for second‐order systems discretized by the h ‐version of the finite element method, provided linear interpolation functions are used as admissible functions, the principle is not valid for fourth‐order systems. To characterize the computed eigenvalues for fourth‐order systems discretized by the h ‐version of the finite element method, this paper formulates two bracketing theorems.