Adaptive BEM with optimal convergence rates for the Helmholtz equation

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.

References in corpus (2)

• Adaptive IGAFEM with optimal convergence rates: Hierarchical B-splines
• Adaptive BEM with inexact PCG solver yields almost optimal computational costs

Cited by in corpus (6)

• Mathematical foundations of adaptive isogeometric analysis
• A robust solver for elliptic PDEs in 3D complex geometries
• Adaptive boundary element methods for the computation of the electrostatic capacity on complex polyhedra
• Adaptive BEM for elliptic PDE systems, part II: Isogeometric analysis with hierarchical B-splines for weakly-singular integral equations
• The saturation assumption yields optimal convergence of two-level adaptive BEM
• Adaptive BEM for elliptic PDE systems, Part I: Abstract framework for weakly-singular integral equations