Quasi-Interpolation and A Posteriori Error Analysis in Finite Element Methods

Carstensen, Carsten. "Quasi-Interpolation and A Posteriori Error Analysis in Finite Element Methods." ESAIM: Mathematical Modelling and Numerical Analysis 33.6 (2010): 1187-1202. <http://eudml.org/doc/197513>.

@article{Carstensen2010,
abstract = { One of the main tools in the proof of residual-based a posteriori error estimates is a quasi-interpolation operator due to Clément. We modify this operator in the setting of a partition of unity with the effect that the approximation error has a local average zero. This results in a new residual-based a posteriori error estimate with a volume contribution which is smaller than in the standard estimate. For an elliptic model problem, we discuss applications to conforming, nonconforming and mixed finite element methods. },
author = {Carstensen, Carsten},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {A posteriori error estimates; adaptive algorithm; reliability; mixed finite element method; nonconforming finite element method.; quasi-interpolation; a posteriori error analysis; finite element method; elliptic model problem},
language = {eng},
month = {3},
number = {6},
pages = {1187-1202},
publisher = {EDP Sciences},
title = {Quasi-Interpolation and A Posteriori Error Analysis in Finite Element Methods},
url = {http://eudml.org/doc/197513},
volume = {33},
year = {2010},
}

TY - JOUR
AU - Carstensen, Carsten
TI - Quasi-Interpolation and A Posteriori Error Analysis in Finite Element Methods
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 33
IS - 6
SP - 1187
EP - 1202
AB - One of the main tools in the proof of residual-based a posteriori error estimates is a quasi-interpolation operator due to Clément. We modify this operator in the setting of a partition of unity with the effect that the approximation error has a local average zero. This results in a new residual-based a posteriori error estimate with a volume contribution which is smaller than in the standard estimate. For an elliptic model problem, we discuss applications to conforming, nonconforming and mixed finite element methods.
LA - eng
KW - A posteriori error estimates; adaptive algorithm; reliability; mixed finite element method; nonconforming finite element method.; quasi-interpolation; a posteriori error analysis; finite element method; elliptic model problem
UR - http://eudml.org/doc/197513
ER -