This note deals with the approximation, by a P 1 finite element method with numerical integration,of solution curves of a semilinear problem. Because of both mixed boundary conditions and geometrical properties of the domain, some of the solutions do not belong to H 2. So, classical results for convergence lead to poor estimates. We show how to improve such estimates with the use of weighted Sobolev spaces together with a mesh“a priori adapted” to the singularity. For the H 1 or L 2-norms,we achieve optimal results.