ESAIM: Mathematical Modelling and Numerical Analysis

Research Article

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

Carstensen, Carsten

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


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.

(Received November 27 1997)

(Revised December 9 1998)

(Online publication August 15 2002)

Key Words:

  • A posteriori error estimates;
  • adaptive algorithm;
  • reliability;
  • mixed finite element method;
  • nonconforming finite element method.

Mathematics Subject Classification:

  • 65N30;
  • 65R20;
  • 73C50