High accuracy analysis of the Adini's nonconforming element (Q1599497)

This paper can be viewed as a continuation of the convergence and a priori error estimate studies developed by \textit{P. Lascaux} and \textit{P. Lesaint} [Revue Franc. Automat. Informa. Rech. Operat. 9, Analyse Numer. R-1, 9-53 (1975; Zbl 0319.73042)] and by \textit{M. Wang} [J. Comput. Math. 11, No. 3, 276-288 (1993; Zbl 0796.65110)] on the Adini's nonconforming finite element for solving the biharmonic equation with Dirichlet boundary value conditions. The extensions include an improvement of the \(L^\infty\)-error estimates as well as a superconvergence result. A numerical test validates the theoretical results.