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, Wien, 2018, ISBN: 978-3-902627-11-7, 1 - 30.

English 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.

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.