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C. Carstensen, D. Praetorius:
"Averaging Techniques for BEM";
Talk: BICOM Workshop on Boundary Elements, Brunel University, Uxbridge (invited); 06-16-2005 - 06-17-2005.

Averaging techniques for finite element error control, occasionally
called ZZ estimators for the gradient recovery, enjoy a high
popularity in engineering because of their striking simplicity and
universality. One does not even require a PDE to apply the
non-expensive post-processing routines. Recently averaging techniques
have been mathematically proved to be reliable and efficient for
various applications of the finite element method.

We provide a class of averaging error estimators for boundary
integral equations. Symm's integral equation serves as a model
equation studied both theoretically and numerically. We introduce
several new error estimators which are proven to be reliable and
efficient up to terms of higher order. The higher-order terms depend
on the regularity of the exact solution. Numerical experiments
illustrate the theoretical results and show that the [normally
unknown] error is sharply estimated by the proposed estimators, i.e.
error and estimators almost coincide.