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arXiv · 1807.11802

Adaptive BEM with optimal convergence rates for the Helmholtz equation

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.

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Alex Bespalov, Timo Betcke, Alexander Haberl, Dirk Praetorius. 2018-07-31. Adaptive BEM with optimal convergence rates for the Helmholtz equation. https://doi.org/10.1016/j.cma.2018.12.006

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