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For a nonconforming finite element approximation of an elliptic model problem, we propose a posteriori error estimates in the energy norm which use as an additive term the “post-processing error” between the original nonconforming finite element solution and an easy computable conforming approximation of that solution. Thus, for the error analysis, the existing theory from the conforming case can be used together with some simple additional arguments. As an essential point, the property is exploited that the nonconforming finite element space contains as a subspace a conforming finite element space of first order. This property is fulfilled for many known nonconforming spaces. We prove local lower and global upper a posteriori error estimates for an enhanced error measure which is the discretization error in the discrete energy norm plus the error of the best representation of the exact solution by a function in the conforming space used for the post-processing. We demonstrate that the idea to use a computed conforming approximation of the nonconforming solution can be applied also to derive an a posteriori error estimate for a linear functional of the solution which represents some quantity of physical interest.
@article{M2AN_2002__36_3_489_0,
author = {Schieweck, Friedhelm},
title = {A posteriori error estimates with post-processing for nonconforming finite elements},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {489--503},
publisher = {EDP-Sciences},
volume = {36},
number = {3},
year = {2002},
doi = {10.1051/m2an:2002022},
mrnumber = {1918941},
zbl = {1041.65083},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an:2002022/}
}
TY - JOUR AU - Schieweck, Friedhelm TI - A posteriori error estimates with post-processing for nonconforming finite elements JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2002 SP - 489 EP - 503 VL - 36 IS - 3 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/m2an:2002022/ DO - 10.1051/m2an:2002022 LA - en ID - M2AN_2002__36_3_489_0 ER -
%0 Journal Article %A Schieweck, Friedhelm %T A posteriori error estimates with post-processing for nonconforming finite elements %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2002 %P 489-503 %V 36 %N 3 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/m2an:2002022/ %R 10.1051/m2an:2002022 %G en %F M2AN_2002__36_3_489_0
Schieweck, Friedhelm. A posteriori error estimates with post-processing for nonconforming finite elements. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 36 (2002) no. 3, pp. 489-503. doi: 10.1051/m2an:2002022
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