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

Published online by Cambridge University Press:  15 August 2002

Carsten Carstensen*
Mathematisches Seminar, Christian-Albrechts-Universität zu Kiel, Ludewig-Meyn-Str. 4, 24098 Kiel, Germany.
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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.

Research Article
© EDP Sciences, SMAI, 1999

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