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Mathematics > Numerical Analysis

arXiv:1807.11802 (math)
[Submitted on 31 Jul 2018 (v1), last revised 5 Dec 2018 (this version, v3)]

Title:Adaptive BEM with optimal convergence rates for the Helmholtz equation

Authors:Alex Bespalov, Timo Betcke, Alexander Haberl, Dirk Praetorius
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Abstract:We analyze an adaptive boundary element method for the weakly-singular and hypersingular integral equations for the 2D and 3D Helmholtz problem. The proposed adaptive algorithm is steered by a residual error estimator and does not rely on any a priori information that the underlying meshes are sufficiently fine. We prove convergence of the error estimator with optimal algebraic rates, independently of the (coarse) initial mesh. As a technical contribution, we prove certain local inverse-type estimates for the boundary integral operators associated with the Helmholtz equation.
Subjects: Numerical Analysis (math.NA)
Cite as: arXiv:1807.11802 [math.NA]
  (or arXiv:1807.11802v3 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.1807.11802
Journal reference: Computer Methods in Applied Mechanics and Engineering, 346 (2019), 260-287
Related DOI: https://doi.org/10.1016/j.cma.2018.12.006

Submission history

From: Alexander Haberl [view email]
[v1] Tue, 31 Jul 2018 13:19:05 UTC (2,277 KB)
[v2] Wed, 8 Aug 2018 07:30:19 UTC (2,277 KB)
[v3] Wed, 5 Dec 2018 13:39:37 UTC (1,076 KB)
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