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

Abstract

Abstract. In our paper [3], we considered the acoustic and electromagneticscat-tering problems in three spatial dimensions. In particular, we studieda perfectlymatched layer (PML) approximation to an electromagnetic scatteringproblem. Wedemonstrated both the solvability of the continuous PML approximationsand the ex-ponential convergence of the resulting solution to the solution ofthe original acousticor electromagnetic problem as the layer increased.In this paper, we consider finite element approximation of the truncatedPML elec-tromagnetic scattering problem. Specifically, we consider approximationswhich resultfrom the use of Nedelec (edge) finite elements. We show that the resultingfinite ele-ment problem is stable and gives rise to quasi-optimal convergencewhen the mesh sizeis su?ciently small.