Error Analysis for the Finite Element Approximation of Transmission Eigenvalues
Abstract
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.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jul 24, 2014
- Source ID
- 10.1515/cmam-2014-0021
Entities
People
- Fioralba Cakoni
- Jiguang Sun
- Peter Monk
Organizations
- Air Force Office of Scientific Research
- Michigan Technological University
- National Science Foundation
- United States Army Research Laboratory
- University of Delaware