97-11   Berichtsreihe des Mathematischen Seminars der Universität Kiel

Carsten Carstensen, Stefan A. Funken:

Constants in Clement-interpolation error and residual based a posteriori estimates in finite element methods

Residual based adaptive finite element methods involve constants in front of a weighted volume term and in front of weighted stress jumps across inner-element boundaries. It is well-known and usually stated that those constants depend on the shape of the elements only. Although they are believed to be of order O(1), these constants are usually not calculated. In particular, the different or equal weighting of the two contributions to the error indicator used in adaptive mesh-refinement algorithms is not justified.

This paper provides explicit estimates for Clement's interpolation operator and consequently for the two constants. The computable bounds for these constants are derived in terms of the mesh geometry and so put the final piece to a fully reliable a posteriori finite element error analysis.

Mathematics Subject Classification (1991): 65N30, 35J70, 73C60

Bibliographical note: to appear in East-West Journal of Numerical Analysis

Keywords: a posteriori error estimates, adaptive algorithms, reliability, Poincare's inequality, Friedrichs' inequality


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