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M. Karkulik, D. Praetorius:
"Application of Interpolation theory to adaptive 3D-BEM";
Talk: 8th Söllerhaus Workshop on Fast Boundary Element Methods in Industrial Applications, Hirschegg/Kleinwalsertal; 09-30-2010 - 10-03-2010.

Recently, we proved the convergence of an adaptive
boundary element method for the Dirichlet problem in two dimensions.
In our talk, we show how the analysis therein can be extended to three dimensions.
We first show how the K-Method of the theory of interpolation spaces
can be used to obtain approximation properties of a certain class
of quasi-interpolation operators in fractional order Sobolev spaces, even
for adaptively generated meshes.
Then, we use this approach to show convergence of a data-perturbed
boundary element method for the Dirichlet problem in three dimensions.