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A Galerkin method with modified piecewise polynomials for solving a second-order boundary value problem

par Hallet, P.;Hennart, Jean Pierre;Mund, Ernest
Référence Numerische Mathematik, 27, 1, page (11-20)
Publication Publié, 1976-03

Article révisé par les pairs

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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.