00-6   Berichtsreihe des Mathematischen Seminars der Universität Kiel

Carsten Carstensen, Stefan A. Funken:

Averaging Technique for FE-A~Posteriori Error Control in Elasticity. Part II: $\lambda$-independent estimates

In the second part of our investigations on a~posteriori error estimates and a~posteriori error control in finite element analysis in elasticity we focus on robust a~posteriori error bounds. First we establish a residual-based a~posteriori error estimate which is reliable and efficient up to higher order terms and $\lambda$-independent multiplicative constants; the Lam\'e constant $\lambda$ steers the incompressibility. Second we show the robust efficiency and reliability of averaging techniques in certain norms. Numerical evidence supports that the reliability depends on the smoothness of given right-hand sides and is 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, locking


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