00-11   Berichtsreihe des Mathematischen Seminars der Universität Kiel

Carsten Carstensen, Stefan A. Funken:

Averaging Technique for A Posteriori Error Control in Elasticity. Part III: Locking-free nonconforming FEM

In the third part of our investigations on averaging techniques for a~posteriori error control in elasticity we focus on nonconforming finite elements in two dimensions. Kouhia and Stenberg (\textit{Comput. Meth. Appl. Mech. Engrg.} \textbf{124} (1995) 195--212) established robust a~priori error estimates for a Galerkin-discretisation where the first component of the discrete displacement function is discretised with conforming and the second with nonconforming $P1$ finite elements. Here we study robust, i.e., $\lambda$-independent reliability and efficiency estimates for averaging error estimators. Numerical evidence supports that the reliability depends on the smoothness of given right-hand sides and independent of the structure of a shape-regular mesh.

Mathematics Subject Classification (1991): 65N30, 65R20, 73C50

Keywords: elasticity, a posteriori error estimates, adaptive algorithm, reliability, finite element method, nonconforming finite elements

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