Adaptive BEM with optimal convergence rates for the Helmholtz equation
Numerical Analysis
2019-03-21 v3
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.
Cite
@article{arxiv.1807.11802,
title = {Adaptive BEM with optimal convergence rates for the Helmholtz equation},
author = {Alex Bespalov and Timo Betcke and Alexander Haberl and Dirk Praetorius},
journal= {arXiv preprint arXiv:1807.11802},
year = {2019}
}