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— We analyse the assumed stresses hybrid approximation of the biharmonic problem. We provide optimal error bounds for the displacements in the L-norm and in the energy norm. Résumé. — On analyse une approximation du problème biharmonique par éléments finis hybrides du type « assumed stresses ». On donne une estimation optimale de Verreur pour les déplacements, dans la norme L et dans la norme de Vénergie. INTRODUCTION In this paper we consider the assumed stresses (or dual) hybrid methods due to Pian and Tong (see [10]) for the approximation of the model problem: (P) weHl(Q), Aw = p in Q, where Q is a bounded convex polygonal domain of U and peL(Q). For any regular décomposition $*h of Q the problem (P) is translated mto a saddle point problem in which two unknowns are independently approximated: (i) a function \j/ biharmonic at the interior of any Ke$~h, having the same traces of w on the internai boundaries { ÔK }; (ii) the field o = (oiJ) {i,j=l, 2) of the second derivatives of w inside each K, The numerical analysis of such a method has been done in [3]; a very large family of discretizations is constructed and sufficient conditions are given in order to have convergence. Moreover, if \)/ft and oh are the approximate solutions, optimal error bounds for \|/-\|/fc and o — oh in the norms of HQ(Q) and L(Q) are found. Hère we study the order of convergence of \|/ — v|/h in the L -norm. Let v = v(Q)e]0, 1] be a real number such that: if OeHl(Q) and AQ>sL(Q) then 3> e H l (Q) n H + v (Q). Setting E = \|/ \|/ h we prove that (*) Reçu le 26 octobre 1978. (M Laboratório di Analisi numenca del Consiglio nazionale délie Ricerche, Pavia. Italie. R.A.I.R.O. Analyse numérique/Numerical Analysis, 0399-0516/1979/355/$ 4.00 © Bordas-Dunod

Error estimates for the assumed stresses hybrid methods in the approximation of 4th order elliptic equations