[en] This report is a contribution to the actions destined to improve the numerical treatment of the convection term into the Navier-stokes equations using finite elements technique like N3S software. It concerns the study of two alternative methods, different of the characteristic method usually employed. These methods are variational methods, compatible with the treatment of the Stokes problem: a SUPG method (Streamline Upwind Petrov-Galerkin) and an UPWIND one order method directly deduced from finite differences. Actually, the SUPG method is one of the most employed method to obtain a stable numerical treatment of flow dominated by convection effects, using a variational formulation with finite elements. The UPWIND method proposed consists in using an upwind scheme taking into account the upwind element and computing locally in a linear way the information. A combination of both SUPG and UPWIND methods is proposed. Numerical techniques employed are detailed. Results concerning test cases usually used to validate numerical schemes solving a pure convention equation and Navier-Stokes test cases (incompressible and compressible) are then presented. Comparisons with the characteristic method employed into the N3S code are also presented. (authors). 10 refs