| Issue |
ESAIM: M2AN
Volume 33, Number 6, November December 1999
|
|
|---|---|---|
| Page(s) | 1187 - 1202 | |
| DOI | https://doi.org/10.1051/m2an:1999140 | |
| Published online | 15 August 2002 | |
Quasi-Interpolation and A Posteriori Error Analysis in Finite Element Methods
Mathematisches Seminar,
Christian-Albrechts-Universität zu Kiel,
Ludewig-Meyn-Str. 4, 24098 Kiel, Germany. cc@numerik.uni-kiel.de.
Received:
27
November
1997
Revised:
9
December
1998
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.
Mathematics Subject Classification: 65N30 / 65R20 / 73C50
Key words: A posteriori error estimates / adaptive algorithm / reliability / mixed finite element method / nonconforming finite element method.
© EDP Sciences, SMAI, 1999
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