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P. Goldenits:
"Adaptive Mesh-Refinement for a Hypersingular Integral Equation in 2D";
Talk: PDETech Seminar Talk, TU Wien; 2009-03-19.

The 2D Laplace equation with Neumann boundary conditions can
equivalently be stated as a first-kind integral equation $Wu = F$
with hypersingular integral operator $W$ and certain right-hand
side $F$. For this integral equation, we discuss adaptive mesh-refinement
based on the (h-h/2)-error estimator, well-known from the context
of ordinary differential equations. With the help of basic functional
analysis, it is easy to see that any mesh-refinement based algorithm
leads to a convergent sequence $(u_n)$ of discrete solutions. However,
the limit $u_\infty$ is not apriori known to coincide with the exact
solution $u$. We finally analyze the convergence of this adaptive
algorithm.

BEM, Adaptive Algorithm, Refinement, Error Estimation, Hypersingular Integral Equation