# Quasi-optimal Convergence Rate for an Adaptive Boundary Element Method

@article{Feischl2013QuasioptimalCR, title={Quasi-optimal Convergence Rate for an Adaptive Boundary Element Method}, author={Michael Feischl and Michael Karkulik and Jens Markus Melenk and Dirk Praetorius}, journal={SIAM J. Numer. Anal.}, year={2013}, volume={51}, pages={1327-1348} }

For the simple layer potential $V$ associated with the three-dimensional (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…

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