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Averaging technique for FE – a posteriori error control in elasticity. Part I: Conforming FEM

✍ Scribed by Carsten Carstensen; Stefan A. Funken

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
772 KB
Volume
190
Category
Article
ISSN
0045-7825

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✦ Synopsis

Averaging techniques are popular tools in adaptive ®nite element methods for the numerical treatment of second-order partial dierential equations since they provide ecient a posteriori error estimates by a simple postprocessing. In this paper, the reliability of any averaging estimator is shown for low order ®nite element methods in elasticity. Theoretical and numerical evidence supports that the reliability is up to the smoothness of given right-hand sides and independent of the structure of a shape-regular mesh.

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Averaging technique for a posteriori error control in elasticity. Part III: Locking-free nonconforming FEM
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In the second part of our investigation on a posteriori error estimates and a posteriori error control in ®nite 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 ecient up to higher-orde