Error analysis for the finite element approximation of transmission eigenvalues
Document Type
Article
Publication Date
1-1-2014
Abstract
© De Gruyter 2014. In this paper we consider the transmission eigenvalue problem corresponding to acoustic scattering by a bounded isotropic inhomogeneous object in two dimensions. This is a non-self-adjoint eigenvalue problem for a quadratic pencil of operators. In particular we are concerned with theoretical error analysis of a finite element method for computing the eigenvalues and corresponding eigenfunctions. Our analysis of convergence makes use of Osborn's perturbation theory for eigenvalues of non-self-adjoint compact operators. Some numerical examples are presented to confirm our theoretical error analysis.
Publication Title
Computational Methods in Applied Mathematics
Recommended Citation
Cakoni, F.,
Monk, P.,
&
Sun, J.
(2014).
Error analysis for the finite element approximation of transmission eigenvalues.
Computational Methods in Applied Mathematics,
14(4), 419-427.
http://doi.org/10.1515/cmam-2014-0021
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/13457