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C. Carstensen, S. Funken, D. Praetorius:
"Averaging Techniques for BEM";
Talk: IABEM 2006 Conference, Graz; 07-10-2006 - 07-12-2006.

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.

In our talk we establish a class of averaging error estimators for
boundary integral methods. Symm's integral equation of the first
kind with a non-local single-layer integral operator serves as a
model equation studied both theoretically and numerically. The
introduced error estimators are 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.

[This contribution got the 2nd prize in the Young Researcher Award
at IABEM 2006.]

http://www.math.tuwien.ac.at/~dirk/download/talk/iabem2006.pdf