M. Feischl, M. Karkulik, J. Melenk, D. Praetorius:
"Quasi-optimal convergence rate for an adaptive boundary element method";
SIAM Journal on Numerical Analysis, 51 (2013), 2; S. 1327 - 1348.

Kurzfassung englisch:
For the simple layer potential V
that is associated with the 3D Laplacian, we consider the weakly
singular integral equation V\phi=f.
This equation is discretized by the lowest order Galerkin boundary
element method.
We prove convergence of an h-adaptive algorithm that is driven by a
weighted residual error estimator. Moreover, we identify the
approximation class for which the adaptive algorithm converges
quasi-optimally with respect to the number of elements. In particular,
we prove that adaptive mesh refinement is superior to uniform mesh

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