Quasi-Interpolation and A Posteriori Error Analysis in Finite Element Methods
Christian-Albrechts-Universität zu Kiel,
Ludewig-Meyn-Str. 4, 24098 Kiel, Germany. firstname.lastname@example.org.
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