Adaptive BEM with optimal convergence rates for the Helmholtz equation

Alex Bespalov, Timo Betcke, Alexander Haberl, Dirk Praetorius

Published 2018-07-31Version 1

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 {\sl a priori} information that the underlying meshes are sufficiently fine. %Instead, adaptive mesh-refinement leads to 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.