M. Feischl, M. Karkulik, J. Melenk, D. Praetorius:

"Quasi-optimal convergence rate for an adaptive boundary element method";

in: "ASC Report 28/2011", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2011, ISBN: 978-3-902627-04-9.

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

refinement.

http://www.asc.tuwien.ac.at/preprint/2011/asc28x2011.pdf

Created from the Publication Database of the Vienna University of Technology.