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M. Aurada, P. Goldenits, D. Praetorius:
"Convergence of data perturbed adaptive boundary element methods";
in: "ASC Report 40/2009", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2009, ISBN: 978-3-902627-02-5.

For the boundary integral formulation of a 2D Laplace equation with Dirichlet
boundary conditions, we consider an adaptive Galerkin BEM based on an
(h−h/2)-type error estimator which, contrary to prior works, includes the
resolution of the perturbed Dirichlet data. Since the analysis of the error
estimator depends crucially on the K-mesh property, we propose a local
mesh-refinement strategy which preserves the K-mesh property and which is
proven to be optimal with respect to the number of generated boundary
elements. We then prove that the usual adaptive algorithm drives the
underlying error estimator 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/2009/asc40x2009.pdf