# An interior penalty discontinuous Galerkin method for the time-domain acoustic-elastic wave interaction problem

## TL;DR

This paper develops and analyzes a symmetric interior penalty discontinuous Galerkin method for simulating time-domain acoustic-elastic wave interactions, providing error estimates and numerical validation.

## Contribution

It introduces a novel DG method for fluid-solid interaction problems with proven error bounds and numerical validation.

## Key findings

- The method achieves high accuracy in simulations.
- Error estimates are rigorously established.
- Numerical results confirm the method's effectiveness.

## Abstract

In this paper, we consider numerical solutions of a time domain acoustic-elastic wave interaction problem which occurs between a bounded penetrable elastic body and a compressible inviscid fluid. It is also called the fluid-solid interaction problem. Firstly, an artificial boundary is introduced to transform the original transmission problem into a problem in a bounded region, and then its well-posed results are presented. We then employ a symmetric interior penalty discontinuous Galerkin method for the solution of the reduced interaction problem consisting of second-order wave equations. A priori error estimate in the energy norm is presented, and numerical results confirm the accuracy and validity of the proposed method.