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Averaging technique for a posteriori error control in elasticity. Part III: Locking-free nonconforming FEM

✍ Scribed by Carsten Carstensen; Stefan A. Funken

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
590 KB
Volume
191
Category
Article
ISSN
0045-7825

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✦ Synopsis

In the third part of our investigations on averaging techniques for a posteriori error control in elasticity we focus on nonconforming ®nite elements in two dimensions. Kouhia and Stenberg [Comput. Methods Appl. Mech. Engrg. 124 (1995) 195] established robust a priori error estimates for a Galerkin-discretisation where the ®rst component of the discrete displacement function is discretised with conforming and the second with nonconforming P 1 ®nite elements. Here we study robust, i.e., k-independent reliability and eciency estimates for averaging error estimators. Numerical evidence supports that the reliability depends on the smoothness of given righthand sides and independent of the structure of a shape-regular mesh.

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Averaging technique for FE – a posterior
Averaging technique for FE – a posteriori error control in elasticity. Part I: Conforming FEM
✍ Carsten Carstensen; Stefan A. Funken 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 772 KB

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

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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