In this paper, we carry out the numerical analysis of adistributed optimal control problem governed by a quasilinearelliptic equation of non-monotone type. The goal is to prove thestrong convergence of the discretization of the problem by finiteelements. The main issue is to get error estimates for thediscretization of the state equation. One of the difficulties inthis analysis is that, in spite of the partial differentialequation has a unique solution for any given control, theuniqueness of a solution for the discrete equation is an openproblem.
