Error analysis for the finite element approximation of transmission eigenvalues
© 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.
Computational Methods in Applied Mathematics
Error analysis for the finite element approximation of transmission eigenvalues.
Computational Methods in Applied Mathematics,
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