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arXiv · 1211.4677

The lower bound of the error estimate in the L2 norm for the Adini element of the biharmonic equation

Jun Hu·Zhongci Shi
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Abstract

This paper is devoted to the $L^2$ norm error estimate of the Adini element for the biharmonic equation. Surprisingly, a lower bound is established which proves that the $ L^2$ norm convergence rate can not be higher than that in the energy norm. This proves the conjecture of [Lascaux and Lesaint, Some nonconforming finite elements for the plate bending problem, RAIRO Anal. Numer. 9 (1975), pp. 9--53.] that the convergence rates in both $L^2$ and $H^1$ norms can not be higher than that in the energy norm for this element.

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Jun Hu, Zhongci Shi. 2012-11-20. The lower bound of the error estimate in the L2 norm for the Adini element of the biharmonic equation. https://arxiv.org/abs/1211.4677

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