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Averaging technique for FE – a posteriori error control in elasticity. Part II: λ-independent estimates

✍ Scribed by Carsten Carstensen; Stefan A. Funken

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

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✦ Synopsis

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-order terms and k-independent multiplicative constants; the Lam e constant k steers the incompressibility. Second we show the robust eciency and reliability of averaging techniques in certain norms. Numerical evidence supports that the reliability of depends on the smoothness of given right-hand sides and is 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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✍ Carsten Carstensen; Stefan A. Funken 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 590 KB

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-