A priori error estimates for a time-dependent boundary element method for the acoustic wave equation in a half-space

TL;DR

This paper develops a priori error estimates for a time-dependent boundary element method solving the acoustic wave equation in a half-space, focusing on mathematical properties of boundary integral operators and Sobolev spaces.

Contribution

It provides new a priori error estimates for a boundary element method applied to wave equations in half-spaces, including analysis for Lipschitz obstacles and screens.

Findings

Derived a priori error estimates for the boundary element method.

Analyzed properties of anisotropic Sobolev spaces and boundary integral operators.

Applicable to wave equations outside Lipschitz obstacles in absorbing half-spaces.

Abstract

We investigate a time-domain Galerkin boundary element method for the wave equation outside a Lipschitz obstacle in an absorbing half-space. A priori estimates are presented for both closed surfaces and screens, and we discuss the relevant properties of anisotropic Sobolev spaces and the boundary integral operators between them.