Nonconforming locking-free finite elements for Reissner-Mindlin plates C. Chinosi a , C. Lovadina b,c and L.D. Marini b,c,1 a Dipartimento di Scienze e Tecnologie Avanzate, Universit` a del Piemonte Orientale, Italy b Dipartimento di Matematica, Universit` a di Pavia, Italy c IMATI-CNR, Pavia, Italy Abstract We prove optimal error estimates in L 2 for a nonconforming finite element for Reissner-Mindlin plates recently introduced in [13]. Moreover, we present numerical experiments using this element and other two nonconforming elements analyzed in [8]. Key words: Finite Element Methods, Reissner-Mindlin plates, Nonconforming Methods, Error Analysis. Introduction In recent times there has been a considerable interest in the extension of Dis- continuous Galerkin methods to the treatment of elliptic problems for various applications (see, for instance, [3] and the references therein). One of the rea- son of this increasing popularity is probably the fact that the DG machinery often implies a different approach to the problem, that can sometimes lead, in the end, to new conforming or nonconforming finite elements that would have been more difficult to discover starting with the classical approach. This is surely the case, for instance, of the extension of the Crouzeix-Raviart element 1 Corresponding author. Address: Dipartimento di Matematica, Universit` a di Pavia. Via Ferrata 1, I-27100, Italy. Tel.: ++39-0382-505638. Fax: ++39-0382-505602 E-mail: marini@imati.cnr.it Preprint submitted to Elsevier Science 5 July 2005