On a Finite Element Method for Solving the Neutron Transport Equation Publications des séminaires de mathématiques et informatique de Rennes, 1974, fascicule S4 « Journées éléments finis », , p. 1-40 © Département de mathématiques et informatique, université de Rennes, 1974, tous droits réservés. L'accès aux archives de la série « Publications mathématiques et informatiques de Rennes » implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/

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Abstract. A finite difference method for the solution of symmetric positive differential equations has already been developped (Katsanis [4]). The finite difference solutions where shown to converge at the rate O (h 89 as h approaches zero, h being the maximum distance between two adjacent mesh points. Here we try to get a better rate of convergence, using a Rayteigh Ritz Galerkin method.We first give a "weak" formulation of the equations, slightly different from the usual one (Friedrichs [3]), in order to take into account the boundary conditions.We define a finite dimensional subspace V h of H 1 (~), in which we look for an approximate solution u h. We show that when the exact solution u is smooth enough, we get the error estimate: where I. t denotes the Euclidean norm in R P. Thus, as is the case for elliptic or parabolic equations, the problem of estimating the error is reduced to questions in approximation theory. When those results are applied to finite element methods, with polynomial approximations of degree =

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