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Talks and Poster Presentations (without Proceedings-Entry):

C. Carstensen, D. Praetorius:
"Averaging Techniques for the Effective Numerical Solution of Integral Equations of the First Kind";
Talk: Workshop on Advanced Scientific Computing and Applications, Györ, Ungarn (invited); 10-22-2004.



English abstract:
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.

In this 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. We provide 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.

Created from the Publication Database of the Vienna University of Technology.