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Eng Anal Bound Elem. 2014 Jan;38(100):49-60.

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

Author information

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

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