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

by   Gustav Ludvigsson, et al.

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.


page 25

page 27


Energy-preserving mixed finite element methods for the Hodge wave equation

Energy-preserving numerical methods for solving the Hodge wave equation ...

High-order mass- and energy-conserving SAV-Gauss collocation finite element methods for the nonlinear Schrödinger equation

A family of arbitrarily high-order fully discrete space-time finite elem...

A high order explicit time finite element method for the acoustic wave equation with discontinuous coefficients

In this paper, we propose a novel high order explicit time discretizatio...

A conservative and energy stable discontinuous spectral element method for the shifted wave equation in second order form

In this paper, we develop a provably energy stable and conservative disc...

Analysis and application of an overlapped FEM-BEM for wave propagation in unbounded and heterogeneous media

An overlapped continuous model framework, for the Helmholtz wave propaga...

Energy decay analysis for Porous elastic system with microtemperature : A second spectrum approach

In this work, we analyze porous elastic system with microtemperature fro...

Quasi-Monte Carlo finite element analysis for wave propagation in heterogeneous random media

We propose and analyze a quasi-Monte Carlo (QMC) algorithm for efficient...