Article révisé par les pairs
Résumé : The classical Ritz-Galerkin method is applied to a linear, second-order, self-adjoint boundary value problem. The coefficient functions of the operator exhibit a piecewise smooth behaviour characteristic of some "physical" situations. A trial function is constructed using a modified quintic smooth Hermite space {Mathematical expression}, in order to meet some desired regularity conditions for the approximate solution. A collocation technique is used to reduce the amount of computational work. Known convergence properties for the projection method are recalled which, in this particular case, are illustrated by a series of numerical experiments. © 1976 Springer-Verlag.