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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63 Citations

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