We develop implicit a posteriori error estimators for elliptic boundary value problems. Local problems are formulated for the error and the corresponding Neumann type boundary conditions are approximated using a new family of gradient averaging procedures. Convergence properties of the implicit error estimator are discussed independently of residual type error estimators, and this gives a freedom in the choice of boundary conditions. General assumptions are elaborated for the gradient averaging which define a family of implicit a posteriori error estimators. We will demonstrate the performance and the favor of the method through numerical experiments.
@article{bwmeta1.element.doi-10_2478_s11533-011-0119-7,
author = {Tam\'as Horv\'ath and Ferenc Izs\'ak},
title = {Implicit a posteriori error estimation using patch recovery techniques},
journal = {Open Mathematics},
volume = {10},
year = {2012},
pages = {55-72},
zbl = {1247.65141},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0119-7}
}
Tamás Horváth; Ferenc Izsák. Implicit a posteriori error estimation using patch recovery techniques. Open Mathematics, Tome 10 (2012) pp. 55-72. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0119-7/
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