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M. Feischl, T. Führer, G. Gantner, A. Haberl, D. Praetorius:
"Adaptive boundary element methods for optimal convergence of point errors";
in: "ASC Report 34/2014", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2014, ISBN: 978-3-902627-07-0, 1 - 22.

One particular strength of the boundary element method is that it allows for a high-order
pointwise approximation of the solution of the related partial differential equation via the
representation formula. However, the high-order convergence and hence accuracy
usually suffers from singularities of the Cauchy data. We propose two adaptive
mesh-refining algorithms and prove their quasi-optimal convergence behavior with
respect to the point error in the representation formula. Numerical examples for the
weakly-singular integral equations for the 2D and 3D Laplacian underline our theoretical
findings.

adaptive boundary element method, optimal convergence rates, point error, goal-oriented algorithm.

http://www.asc.tuwien.ac.at/preprint/2014/asc34x2014.pdf