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

Heiko Gimperlein; Ceyhun Özdemir; David Stark; Ernst P. Stephan

doi:10.1007/s00211-020-01142-y

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

Heiko Gimperlein, Ceyhun Özdemir, David Stark, Ernst P. Stephan

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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.

Original language	English
Pages (from-to)	239-280
Number of pages	42
Journal	Numerische Mathematik
Volume	146
Issue number	2
Early online date	25 Aug 2020
DOIs	https://doi.org/10.1007/s00211-020-01142-y
Publication status	Published - Oct 2020

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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This is a post-peer-review, pre-copyedit version of an article published in Numerische Mathematik. The final authenticated version is available online at: http://dx.doi.org/10.1007/s00211-020-01142-y
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https://arxiv.org/pdf/2008.04297.pdf

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AB - 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.

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

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