M. Aurada, P. Goldenits, D. Praetorius:

"Convergence of data perturbed adaptive boundary element methods";

in: "ASC Report 40/2009", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2009, ISBN: 978-3-902627-02-5.

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

boundary conditions, we consider an adaptive Galerkin BEM based on an

(h−h/2)-type error estimator which, contrary to prior works, includes the

resolution of the perturbed Dirichlet data. Since the analysis of the error

estimator depends crucially on the K-mesh property, we propose a local

mesh-refinement strategy which preserves the K-mesh property and which is

proven to be optimal with respect to the number of generated boundary

elements. We then prove that the usual adaptive algorithm drives the

underlying error estimator 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/2009/asc40x2009.pdf

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