Numerical scheme for differential inclusions with maximal monotone term

Let V --> H --> V' be three separable Hilbert spaces. In this Note, we stud y the order of convergence of a,numerical approximation of the problem: (u)over dot Bu + Au There Exists f(., u), u(0) = u(0), where B is a Lipschitz continuous and V-elliptic operator from V to V' and A is a maximal monotone graph in V x V'. If f is Lipschitz continuos from [ 0, T] x H in V' with respect to its second argumeilt and if the section A(0 ) of A is bounded, then the numerical scheme Up+1-U-p/h + B(Up+1) + A(Up+1) There Exists f(ph,U-p), is of order 1/2. Under particular assumptions, it is of order one. (C) 2000 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.