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This paper is devoted to the L2 norm error estimate of the Adini element for the biharmonic equation. Surprisingly, a lower bound is established which proves that the L2 norm convergence rate cannot be higher than that in the energy norm. This proves the conjecture of [Lascaux and Lesaint, RAIRO Anal. Numer., 9 (1975), pp. 9-53] that the convergence rates in both L2 and H1 norms cannot be higher than that in the energy norm for this element. © 2013 Society for Industrial and Applied Mathematics.

A Lower Bound of the $L^2$ Norm Error Estimate for the Adini Element of the Biharmonic Equation