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.
Funding source: Air Force Office of Scientific Research
Award Identifier / Grant number: FA9550-13-1-0199
Funding source: NSF
Award Identifier / Grant number: DMS-1016092
Funding source: US Army Research Laboratory and US Army Research Office
Award Identifier / Grant number: W911NF-11-2-0046
© 2014 by De Gruyter
