A residual a posteriori error estimate for the time-domain boundary element method

TL;DR

This paper develops reliable residual a posteriori error estimates for time-dependent boundary element methods solving the wave equation, enabling adaptive mesh refinement that achieves optimal convergence rates in 3D.

Contribution

It introduces a new residual a posteriori error estimate applicable to a broad class of discretizations for the wave equation.

Findings

Error estimates are reliable for Dirichlet and acoustic boundary conditions.

Numerical examples confirm the theoretical error bounds.

Adaptive mesh refinement achieves optimal convergence rates in 3D.

Abstract

This article investigates residual a posteriori error estimates and adaptive mesh refinements for time-dependent boundary element methods for the wave equation. We obtain reliable estimates for Dirichlet and acoustic boundary conditions which hold for a large class of discretizations. Efficiency of the error estimate is shown for a natural discretization of low order. Numerical examples confirm the theoretical results. The resulting adaptive mesh refinement procedures in 3d recover the adaptive convergence rates known for elliptic problems.