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M. Aurada, P. Goldenits, M. Karkulik, D. Praetorius:
"Adaptive BEM for some Mixed Boundary Value Problem";
Talk: 17th ÖMG Congress / Annual DMV Conference, Graz; 09-21-2009 - 09-25-2009.

In our talk, we consider an adaptive BE scheme for the equivalent integral
formulation of the Laplace equation in 2D with mixed boundary conditions. In
the proposed scheme, the given boundary data and the non-homogeneous volume
force are appropriately approximated by piecewise polynomials. Besides the
possible singularities of the (in general unknown) solution, the adaptive
mesh-refinement aims at a sufficient resolution of the data. We prove that
the adaptive algorithm drives an extended estimator quantity, given as sum of
an $h-h/2$-type error estimator and data oscillations, to zero. Under certain assumptions,
this implies that the sequence of (computed) discrete solutions, in fact,
tends to the (unknown) exact solution.

BEM, adaptive, Mixed Boundary Value Problem, A Posteriori