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

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

Applied Numerical Mathematics,62(2012), 4; 226 - 245.

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 algorithm 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 in the energy norm.

http://dx.doi.org/10.1016/j.apnum.2011.03.008

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