Estimation d'erreur d'une méthode de volumes-éléments finis stabilisée appliquée au problème de Stokes stationnaire et transient

The present report addresses the rigorous study of convergence of a stabilized finite volume element method applied to stationary and time dependent Stokes problems. Some preliminary results about the existence and uniqueness of solution at continuous and discrete level are provided for stabilized finite element and finite volume element formulations when using two different stabilization techniques, and then we prove consistency of the methods for the time-independent and time-dependent problems, and derive optimal convergence rates.