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— We consider a second order real elliptic Dirichlet problem in a bounded plane smooth domain, Lu = f in fi œ Ry u — 0 on dQ. For its numerical solution we employ the finite element method with quadratic triangular isoparametric éléments combined with a numerical intégration procedure involving function values at three nodal points in each element. We prove that iffhas third order derivatives in Ly and if the séquence of finite element partitions is quasi-uniform with the maximum diameter of any element for a certain partition being essentially h, then with uh denoting the approximate solution we have max\u(x)-uh(x)\ ^ C . A 3 | | / | | ^ Î . Hère s is an arbitrarily smallpositive number, and CB does not depend on h or f 1. THE NUMERICAL PROCEDURE AND THE MAIN RESULT In this section we shall present the problem which we want to solve, define precisely our method for finding an approximate solution, and state our error estimâtes (in Theorem 1.1). After giving some références to related work we proceed to prove Theorem 1.1 using certain auxiliary results which will be verified in the remaining sections of the paper. The following conventions will be used throughout this paper. The letter C will dénote a generic constant, and e will be used for an arbitrarily small positive number, often subject to a non-essential change. Generic constants C may depend on £ without explicit mention. (*) Manuscrit reçu le 21 avril 1977. l) Supported in part by the National Science Foundation, U.S.A. () Department of Mathematics, White Hall, Cornell University, Ithaca, U.S.A. R.A.I.R.O. Analyse numérique/Numerical Analysis, vol. 12, n° 2, 1978

Maximum norm error estimates in the finite element method with isoparametric quadratic elements and numerical integration