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- Title
Local and parallel finite element method for solving the biharmonic eigenvalue problem of plate vibration.
- Authors
Zhao, Ruilin; Yang, Yidu; Bi, Hai
- Abstract
In this paper, we establish a new local and parallel finite element discrete scheme based on the shifted‐inverse power method for solving the biharmonic eigenvalue problem of plate vibration. We prove the local error estimation of finite element solution for the biharmonic equation/eigenvalue problem and prove the error estimation of approximate solution obtained by the local and parallel scheme. When the diameters of three grids satisfy H4 = ϑ(w2) = ϑ(h), the approximate solutions obtained by our schemes can achieve the asymptotically optimal accuracy. The numerical experiments show that the computational schemes proposed in this paper are effective to solve the biharmonic eigenvalue problem of plate vibration.
- Subjects
BIHARMONIC equations; EIGENVALUES; FINITE element method; VOLTERRA equations; GALERKIN methods
- Publication
Numerical Methods for Partial Differential Equations, 2019, Vol 35, Issue 2, p851
- ISSN
0749-159X
- Publication type
Article
- DOI
10.1002/num.22329