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C. Carstensen, D. Praetorius:
"Averaging Techniques for A Posteriori Error Control in Finite Element and Boundary Element Analysis";
Lecture Notes in Applied and Computational Mechanics (invited), 29 (2007), 29 - 59.

Averaging techniques for a posteriori error control are established
for differential and integral equations within a unifying setting.
The reliability and efficiency of the introduced estimator results
from two grids $\TT_h$ and $\TT_H$ with different polynomial degrees
for a smooth exact solution. The proofs are based on first order
approximation operators and inverse estimates. For a finer and finer
fine mesh $\TT_h$, the estimator becomes asymptotically exact. The
abstract framework is applicable to a finite element method for the
Laplace equation, boundary element methods for Symm's and the
hypersingular integral equation or transmission problems.

http://dx.doi.org/10.1007/978-3-540-47533-0_2

http://www.math.tuwien.ac.at/~dirk/download/preprint/ccdpr9.pdf