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M. Aurada, S. Ferraz-Leite, P. Goldenits, M. Karkulik, M. Mayr, D. Praetorius:
"Convergence of adaptive BEM for some mixed boundary value problem";
in: "ASC Report 12/2010", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2010, ISBN: 978-3-902627-03-2.

For a boundary integral formulation of the 2D Laplace equation with
mixed boundary conditions, we consider an adaptive Galerkin BEM based
on an (h-h/2)-type error estimator. We include the resolution of the
Dirichlet, Neumann, and volume data into the adaptive algorithm. In
particular, an implementation of the developed algorithms has only to
deal with discrete integral operators. We prove that the proposed
adaptive scheme leads to a sequence of discrete solutions, for which
the corresponding error estimators tend to zero. Under a saturation
assumption for the non-perturbed problem which is observed empirically,
the sequence of discrete solutions thus converges to the exact solution
within the energy norm.

http://www.asc.tuwien.ac.at/preprint/2010/asc12x2010.pdf