Résolution approchée de problèmes aux limites elliptiques par des schémas aux éléments finis a plusieurs fonctions arbitraires

Summary The present paper is devoted to the approximate solution of variational elliptic boundary value problems of the form: α(u, v)=(f, v)v ∈V by using approximations of the Hilbert spaceV with several degrees of freedom as constructed in a preceding paper 7]. These approximations lead to finite difference schemes involving several arbitrary parameters, whose solution converge to the exact solution of the boundary value problem if the values of these parameters are small enough. This fact can be utilized to diminish the error between the exact and the approximate solution by a suitable choice of these arbitrary parameters, so as to avoid the use of very small step lengths. The method may prove useful in cases where the coercivity constant of the bilinear form α (u, v) is small when compated to its continuity constant, and more generally for problems of the form: α (u, v)−λ (u. v.)=(f, v) where the constant λ is close to an eigenvalue of the boundary value problem.