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C. Carstensen, S. Funken, D. Praetorius:
"Averaging Techniques for BEM";
in: "Book of Abstracts, IABEM 2006 Conference", issued by: Beer G., Langer U., Schanz M., Steinbach O.,; Verlag der Technischen Universität Graz, Graz, 2006, ISBN: 3-902465-23-9, 139 - 142.

The striking simplicity of averaging techniques in a posteriori error control as well as their amazing accuracy in many numerical examples have made them an extremely popular tool in scientific computing over the last decade. The most prominent example is occasionally named after Zienkiewicz and Zhu, and also called gradient recovery. Therein the focus is on the P1 FEM for the Laplace equation on some domain \Omega and some local averaging operator A acting on the piecewise constant gradients p_h = Du_h followed by linear interpolation.

Recently, we have introduced a class of averaging error estimators for boundary integral methods. In our works, an approximation Ap_h is computed as some best approximation of p_h based on a higher-order spline space on some coarser mesh. The theoretic results cover finite element and boundary element methods as well as the coupling of both.

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