title: ZZ-Type a posteriori error estimators for adaptive boundary element methods on a curve.
abstract: In the context of the adaptive finite element method (FEM), ZZ-error estimators named after Zienkiewicz and Zhu (1987) [52] are mathematically well-established and widely used in practice. In this work, we propose and analyze ZZ-type error estimators for the adaptive boundary element method (BEM). We consider weakly singular and hyper-singular integral equations and prove, in particular, convergence of the related adaptive mesh-refining algorithms. Throughout, the theoretical findings are underlined by numerical experiments.
authors.affiliation: Institute for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstr. 8-10/E101/4, 1040 Wien, Austria.
authors.forename: Michael
authors.initials: M
authors.lastname: Feischl
authors.affiliation: Institute for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstr. 8-10/E101/4, 1040 Wien, Austria.
authors.forename: Thomas
authors.initials: T
authors.lastname: Führer
authors.affiliation: Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Avenida Vicuña Mackenna 4860, Santiago, Chile.
authors.forename: Michael
authors.initials: M
authors.lastname: Karkulik
authors.affiliation: Institute for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstr. 8-10/E101/4, 1040 Wien, Austria.
authors.forename: Dirk
authors.initials: D
authors.lastname: Praetorius
keywords: Adaptive algorithm; Boundary element method; Local mesh-refinement; ZZ-type error estimator
references.citation: Appl Numer Math. 2012 Jun;62(6):787-801
references.pmid: 23482248