An application of the Kantorovich theorem to nonlinear finite element analysis

Finite element solutions of strongly nonlinear elliptic boundary value prob lems are considered. In this paper, using the Kantorovich theorem, we show that, if the Frechet derivative of the nonlinear operator defined by the bo undary value problem is an isomorphism at an exact solution, then there exi sts a locally unique finite element solution near the exact solution. Moreo ver, several a priori error estimates are obtained. Mathematics Subject Cla ssification (1991): 65L60, 65N12, 65N15, 65N30.