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This paper presents a stable finite element approximation for the acousticwave equation on second-order form, with perfectly matched layers (PML) at theboundaries. Energy estimates are derived for varying PML damping for both thediscrete and the continuous case. Moreover, a priori error estimates arederived for constant PML damping. Most of the analysis is performed in Laplacespace. Numerical experiments in physical space validate the theoreticalresults.

On energy-stable and high order finite element methods for the wave equation in heterogeneous media with perfectly matched layers