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— The solution ofthefourth order probiem À u = f in Cl, u = öujdv = 0 on dCl, Q, boundedin R, andits Laplacian are approximated by linear finite éléments. L2-and h^-error estimâtes are given. Let Q ç R be a bounded domain with sufficiently smooth boxmdary. We consider the fourth order boundary value probiem Aw = ƒ in Q, 1 u » ôu/dv = 0 on ÔQ J ( 1 ) with feL2. The basic idea of the mixed method considered hère —due to CiarletRaviart [ 3 ] i s to write the équation (1) as a System A M 2 = ƒ in tî, , } (2) ut = dujdv ==0 on 3Q to approxirnatË^/^ and^2-^Î2iltâneousl3Lby suitably chosen subspaces. (Another mixed method can be used if one is interested to approximate u and ail second dcrivatives of u, ïn this context we refer to Brezzi-Raviart [1] and the références given there.) Using finite element spaces of piecewise polynomials of degree r ^ 2 as approximating subspaces the first L2-error estimâtes were given by CiarletRaviart [3], In [9] improved Z^-estimates have been obtained, and in the case of quadratic finite éléments Rannacher [8] proved an L^-estimate. In this note we show that also in the case of linear finite éléments the mixed method approximations are convergent, and we dérive an error estimate in the L2as well as in the L norm. (*) Reçu juillet 1977. (*) Institut fur Angewandte Mathematik, Albert-Ludwigs-Universitât, Freiburg, Fédéral Republic of Germany. R.A.LR.O. Analyse numérique/Numerical Analysis, vol. 12, n° 1, 1978

A mixed method for 4th order problems using linear finite elements