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M. Aurada, S. Ferraz-Leite, D. Praetorius:
"Convergence of Adaptive Boundary Element Methods";
Talk: Computer Methods in Mechanics CMM 2009, Zielona Góra (invited); 05-18-2009 - 05-21-2009; in: "Short Papers of 18th International Conference on Computer Methods in Mechanics", University of Zielona Gora Press, Zielona Gora (2009), ISBN: 978-83-7481-245-0; 113 - 114.

A posteriori error estimators and adaptive mesh-refinement have
themselves proven to be an important tool for scientific computing.
For error control in finite element methods (FEM), there is a broad
variety of a posteriori error estimators available, and convergence
as well as optimality of adaptive FEM is well-studied in the
literature. This is in sharp contrast to the boundary element method
(BEM). Although a posteriori error estimators and adaptive
algorithms are also successfully applied to boundary element
schemes, even convergence of adaptive BEM is hardly understood
mathematically. In our contribution, we present and discuss recent
mathematical results which give first positive answers for adaptive
BEM.

boundary element method, a posteriori error estimate, adaptive mesh-refinement, convergence of adaptive algorithm

http://www.asc.tuwien.ac.at/~dirk/download/published/afp_cmm2009.pdf