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3.1 Introduction: boundary layers, instability of centered schemes.... 13 3.2 Stationary convections: introduction, schemes based on the method of characteristics, upwind schemes, the method of streamline diffusion, Upwinding by discontinuities, upwinding by cells................ 13 3.3 Convection diffusion 1: introduction, theoretical results on the convection-diffusion equation, time approximation................. 13 3.4 Convection diffusion 2: discretisation of the total derivative, the Lax-Wendroff/Taylor-Galerkin scheme, streamline upwinding (SUPG). 13