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

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 33, Issue: 6, page 1187-1202
- ISSN: 0764-583X

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topCarstensen, 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 -

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