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

TL;DR

This paper introduces a high order explicit time finite element method on Cartesian meshes for solving the acoustic wave equation with complex discontinuous coefficients, achieving optimal convergence without penalties.

Contribution

It presents a novel unfitted finite element approach combined with an explicit time discretization for improved accuracy and stability in complex interface problems.

Findings

Achieves optimal convergence without penalty terms.

Provides strong stability and error estimates.

Numerical results confirm theoretical predictions.

Abstract

In this paper, we propose a novel high order unfitted finite element method on Cartesian meshes for solving the acoustic wave equation with discontinuous coefficients having complex interface geometry. The unfitted finite element method does not require any penalty to achieve optimal convergence. We also introduce a new explicit time discretization method for the ODE system resulting from the spatial discretization of the wave equation. The strong stability and optimal $hp$-version error estimates both in time and space are established. Numerical examples confirm our theoretical results.