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M. Halla:
"A new proof of convergence for radial perfectly matched layer discretizations of Helmholtz scattering and resonance problems";
in: "ASC Report 17/2015", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2015, ISBN: 978-3-902627-08-7, 1 - 9.

The analysis of discrete PML approximations is usually split into an
analysis of the modeling error, i.e. the truncation of the PM layer,
and an analysis of the discretization of the truncated problem. We
point out how PML discretizations can be understood as conform-
ing Galerkin discretizations, which allows to apply standard litera-
ture. Thus we present a new proof of convergence for radial PML
discretizations of Helmholtz scattering and resonance problems. We
also derive previously unknown error estimates for the approximation
of resonances. In particular we achieve exponential convergence rates
with respect to the width of the (perfectly matched) layer.

http://www.asc.tuwien.ac.at/preprint/2015/asc17x2015.pdf