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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";
Applied Numerical Mathematics, 62 (2012), 4; 226 - 245.

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 algorithm 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 in the energy norm.

http://dx.doi.org/10.1016/j.apnum.2011.03.008