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M. Feischl, T. Führer, G. Gantner, A. Haberl, D. Praetorius:
"Adaptive BEM for optimal convergence of point errors";
Talk: 11th Austrian Numerical Analysis, Linz; 2015-05-06 - 2015-05-08.

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 the accuracy of
the approximation usually suffer from singularities of the Cauchy data. In our talk which is
based on a recent work of the authors (to appear in Numer. Math., 2015), we propose an
adaptive mesh-refining algorithm and prove its quasi-optimal convergence behavior with
respect to the point error in the representation formula. The analysis uses the abstract framework of [Carstensen, Feischl, Page, Praetorius; Comput. Math. Apple. 2014] to generalize ideas from [Mommer, Stevenson; SIAM J. Numer. Anal. 2009] which proved
optimal convergence of goal-oriented adaptive FEM for the Poisson model problem in
2D. In particular, our approach goes beyond our model problem and also covers a more
general setting for goal-oriented adaptivity in the frame of adaptive finite element or
adaptive boundary element computations.

Numerical examples for the weakly-singular integral equations associated with the 2D
and 3D Laplacian underline our theoretical findings.