This paper presents a stable finite element approximation for the acoustic wave equation on second-order form, with perfectly matched layers (PML) at the boundaries. Energy estimates are derived for varying PML damping for both the discrete and the continuous case. Moreover, a priori error estimates are derived for constant PML damping. Most of the analysis is performed in Laplace space. Numerical experiments in physical space validate the theoretical results.

翻译：本文件为二阶式声波方程式的声波方程式提供了一个稳定的有限元素近似值,在边界处的层层完全吻合(PML),对离散和连续情况的不同PML阻断作用得出能源估计值,此外,对恒定的PML阻断作用也得出先验误差估计值,大部分分析是在Laplace空间进行的,物理空间的数值实验验证了理论结果。