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In our paper (3), we considered the acoustic and electromagnetic scat- tering problems in three spatial dimensions. In particular, we studied a perfectly matched layer (PML) approximation to an electromagnetic scattering problem. We demonstrated both the solvability of the continuous PML approximations and the ex- ponential convergence of the resulting solution to the solution of the original acoustic or electromagnetic problem as the layer increased. In this paper, we consider finite element approximation of the truncated PML elec- tromagnetic scattering problem. Specifically, we consider approximations which result from the use of Nedelec (edge) finite elements. We show that the resulting finite ele- ment problem is stable and gives rise to quasi-optimal convergence when the mesh size is sufficiently small.

Analysis of a finite element PML approximation for the three dimensional time-harmonic Maxwell problem