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.

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