Clément Interpolation and Its Role in Adaptive Finite Element Error Control

  • Carsten Carstensen
Part of the Operator Theory: Advances and Applications book series (OT, volume 168)


Several approximation operators followed Philippe Clément’s seminal paper in 1975 and are hence known as Clément-type interpolation operators, weak-, or quasi-interpolation operators. Those operators map some Sobolev space VW k,p(Ω) onto some finite element space V hW k,p(Ω) and generalize nodal interpolation operators whenever W k,p(Ω) ⊄ C 0(Ω), i.e., when pn/k for a bounded Lipschitz domain Ω ⊂ ℝn. The original motivation was H 2C 0(Ω) for higher dimensions n ≥ 4 and hence nodal interpolation is not well defined.

Todays main use of the approximation operators is for a reliability proof in a posteriori error control. The survey reports on the class of Clément type interpolation operators, its use in a posteriori finite element error control and for coarsening in adaptive mesh design.


Posteriori Error Error Control Posteriori Error Estimation Interpolation Operator Dual Norm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2006

Authors and Affiliations

  • Carsten Carstensen
    • 1
  1. 1.Humboldt-Universität zu BerlinBerlinGermany

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