The goal of this course is to show some fundamental
elements of numerical approximation of partial differential
equations. Linear evolution equations involving transport and diffusion phenomenons which can be observed in most of
mechanical problems are discretized by two methods: finite differences and finite volumes.
Main notions like accuracy, stability, convergence, numerical diffusion and dispersion,
are analyzed. Implementation is carefully studied. The numerical methods presented in the course are studied with
exercices and programming sessions.