A high-order discontinuous Galerkin approach to the elasto-acoustic problem

TL;DR

This paper develops a high-order discontinuous Galerkin method for simulating coupled viscoelastic and acoustic wave problems on polygonal meshes, providing stability, error estimates, and validation through numerical experiments.

Contribution

It introduces a novel high-order DG scheme for elasto-acoustic coupling on polygonal meshes with rigorous stability and error analysis.

Findings

Proved well-posedness of the coupled problem.

Established stability and a priori error estimates.

Validated convergence through numerical experiments.

Abstract

We address the spatial discretization of an evolution problem arising from the coupling of viscoelastic and acoustic wave propagation phenomena by employing a discontinuous Galerkin scheme on polygonal and polyhedral meshes. The coupled nature of the problem is ascribed to suitable transmission conditions imposed at the interface between the solid (elastic) and fluid (acoustic) domains. We state and prove a well-posedness result for the strong formulation of the problem, present a stability analysis for the semi-discrete formulation, and finally prove an a priori $hp$-version error estimate for the resulting formulation in a suitable (mesh-dependent) energy norm. We also discuss the time integration scheme employed to obtain the fully discrete system. The convergence results are validated by numerical experiments carried out in a two-dimensional setting.