A new finite element approach for the Dirichlet eigenvalue problem
Document Type
Article
Publication Date
7-2020
Department
Department of Mathematical Sciences
Abstract
We propose a new finite element approach, which is different than the classic Babuška–Osborn theory, to approximate Dirichlet eigenvalues. The problem is formulated as the eigenvalue problem of a holomorphic Fredholm operator function of index zero. The convergence for conforming finite elements is proved using the abstract approximation theory for holomorphic operator functions. The spectral indicator method is employed to compute the eigenvalues. A numerical example is presented to validate the theory.
Publication Title
Applied Mathematics Letters
Recommended Citation
Xiao, W.,
Gong, B.,
Sun, J.,
&
Zhang, Z.
(2020).
A new finite element approach for the Dirichlet eigenvalue problem.
Applied Mathematics Letters,
105.
http://doi.org/10.1016/j.aml.2020.106295
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/1768