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Eigenvalue convergence in the finite element method
Author(s) -
Bennighof J. K.,
Meirovitch L.
Publication year - 1986
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.1620231112
Subject(s) - eigenvalues and eigenvectors , finite element method , mathematics , convergence (economics) , degree of a polynomial , interpolation (computer graphics) , limiting , hp fem , mixed finite element method , mathematical analysis , polynomial , finite element limit analysis , computer science , structural engineering , physics , engineering , animation , mechanical engineering , quantum mechanics , economics , economic growth , computer graphics (images)
In static force‐deflection applications of the finite element method, convergence rates for the p ‐version, in which the polynomial degree of element interpolation functions is increased while the mesh remains fixed, are superior to those for the h ‐version, in which the element degree remains fixed while the mesh is refined so that element size approaches zero. In structural dynamics applications, one does not seek to approximate a single solution, as in static applications, but seeks estimates for a number of the lower system eigenvalues. This paper identifies factors responsible for poorer accuracy in higher computed eigenvalues. In addition, it explains why the p ‐version of the finite element method can be expected to exhibit significantly better eigenvalue convergence than the h ‐version. Numerical examples demonstrate the superiority of the p ‐version over the h ‐version. They also show the effects of various mechanisms limiting eigenvalue convergence.