M. Aurada, S. Ferraz-Leite, P. Goldenits, M. Karkulik, M. Mayr, D. Praetorius:

"Convergence of adaptive BEM for some mixed boundary value problem";

in: "ASC Report 12/2010", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2010, ISBN: 978-3-902627-03-2.

For a boundary integral formulation of the 2D Laplace equation with

mixed boundary conditions, we consider an adaptive Galerkin BEM based

on an (h-h/2)-type error estimator. We include the resolution of the

Dirichlet, Neumann, and volume data into the adaptive algorithm. In

particular, an implementation of the developed algorithms has only to

deal with discrete integral operators. We prove that the proposed

adaptive scheme leads to a sequence of discrete solutions, for which

the corresponding error estimators tend to zero. Under a saturation

assumption for the non-perturbed problem which is observed empirically,

the sequence of discrete solutions thus converges to the exact solution

within the energy norm.

http://www.asc.tuwien.ac.at/preprint/2010/asc12x2010.pdf

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