Finite dimensional approximation of nonlinear problems

Summary In the first two papers of this series 4, 5], we have studied a general method of approximation of nonsingular solutions and simple limit points of nonlinear equations in a Banach space. We derive here general approximation results of the branches of solutions in the neighborhood of a simple bifurcation point. The abstract theory is applied to the Galerkin approximation of nonlinear variational problems and to a mixed finite element approximation of the von Kármán equations.The work of F. Brezzi has been completed during his stay at the Université P. et M. Curie and at the Ecole PolytechniqueThe work of J. Rappaz has been supported by the Fonds National Suisse de la Recherche Scientifique