ZZ-Type a posteriori error estimators for adaptive boundary element methods on a curve

Michael Feischl; Thomas Führer; Michael Karkulik; Dirk Praetorius

doi:10.1016/j.enganabound.2013.10.008

ZZ-Type a posteriori error estimators for adaptive boundary element methods on a curve

Eng Anal Bound Elem. 2014 Jan;38(100):49-60. doi: 10.1016/j.enganabound.2013.10.008.

Authors

Michael Feischl¹, Thomas Führer¹, Michael Karkulik², Dirk Praetorius¹

Affiliations

¹ Institute for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstr. 8-10/E101/4, 1040 Wien, Austria.
² Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Avenida Vicuña Mackenna 4860, Santiago, Chile.

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.

Keywords: Adaptive algorithm; Boundary element method; Local mesh-refinement; ZZ-type error estimator.