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Approximation and eigenvalue extrapolation of biharmonic eigenvalue problem by nonconforming finite element methods
Author(s) -
Jia Shanghui,
Xie Hehu,
Yin Xiaobo,
Gao Shaoqin
Publication year - 2008
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20268
Subject(s) - biharmonic equation , mathematics , extrapolation , eigenvalues and eigenvectors , finite element method , mathematical analysis , convergence (economics) , divide and conquer eigenvalue algorithm , rate of convergence , boundary value problem , key (lock) , physics , ecology , biology , economics , thermodynamics , economic growth , quantum mechanics
In this paper, we analyze the biharmonic eigenvalue problem by two nonconforming finite elements, Q 1 rotand E Q 1 rot . We obtain full order convergence rate of the eigenvalue approximations for the biharmonic eigenvalue problem based on asymptotic error expansions for these two nonconforming finite elements. Using the technique of eigenvalue error expansion, the technique of integral identities, and the extrapolation method, we can improve the accuracy of the eigenvalue approximations. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008