The main goal of this article is to establish a priori and a posteriori error estimates for the numerical approximation of some non linear ellipticproblems arising in glaciology. The stationary motion of a glacier is givenby a non-Newtonian fluid flow model which becomes, in a firsttwo-dimensional approximation, the so-called infinite parallel sided slabmodel. The approximation of this model is made by a finite element methodwith piecewise polynomial functions of degree 1. Numerical results show thatthe theoretical results we have obtained are almost optimal.
