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

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.

arXiv comment38 pages, 8 figures, to appear in Numerische Mathematik

References in corpus (5)

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• Adaptive time-domain boundary element methods for the wave equation with Neumann boundary conditions
• A Stable Boundary Element Method for Reliable Long-Time Industrial Sound Emission
• Adaptive space-time BEM for the heat equation