A. Bespalov, T. Betcke, A. Haberl, D. Praetorius:
"Adaptive BEM with optimal convergence rates for the Helmholtz equation";
Computer Methods in Applied Mechanics and Engineering, 346 (2019), S. 260 - 287.

Kurzfassung englisch:
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.

boundary element method, Helmholtz equation, a posteriori error estimate, adaptive algorithm, convergence, optimality.

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