Quasi-interpolation and a Posteriori Error Analysis in Finite Element Methods

@inproceedings{Carstensen1999QuasiinterpolationAA,
  title={Quasi-interpolation and a Posteriori Error Analysis in Finite Element Methods},
  author={Carsten Carstensen},
  year={1999}
}
One of the main tools in the proof of residual-based a posteriori error estimates is a quasiinterpolation 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 residualbased 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… CONTINUE READING