Contributions to Books:
A. Bespalov, T. Betcke, A. Haberl, D. Praetorius:
"Adaptive BEM with optimal convergence rates for the Helmholtz equation";
in: "ASC Report 18/2018",
issued by: Institute for Analysis and Scientific Computing;
Vienna University of Technology,
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.
Electronic version of the publication:
Created from the Publication Database of the Vienna University of Technology.