C. Carstensen, D. Praetorius:
"Averaging Techniques for the Effective Numerical Solution of Symm's Integral Equation of the First Kind";
SIAM Journal on Scientific Computing, 27 (2006), 4; S. 1226 - 1260.

Kurzfassung englisch:
Averaging techniques for finite element error control, occasionally
called {\em 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. This paper
establishes 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. We provide four new
error estimators which are proven to be reliable and efficient under
weak assumptions on the discrete spaces. Several 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.

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