Le sujet se compose de deuxprobì emes totalement indépendants. Il compte 8 pages en tout. Chaqueprobì eme està rédiger sur des copies de couleurs distinctes, roses pour leprobì eme 1 et vertes pour leprobì eme 2. Notations et Rappels. On considère Ω un ouvert borné régulier (de classe C ∞) de R d , et L 2 (Ω) l'espace des fonctions de carré intégrable sur Ω. On notera < u, v >= Ω u(x)v(x) dx, e...

We consider a mixed finite element method for the Stokes problem in a polygonal domain Q cz U An inf-sup condition is established which fits into the abstract jramework oj Babuska and Brezzi Using hnear finite éléments, we obtain O{h*)-error estimâtes for the energy norm of the velocity and the L-norm of the pressure The exponent a only dépends on thegreatest intenor angle at a corner of Cl and...

............................................................................................................................................... iRésumé Etendu ................................................................................................................................... iiRéseaux locaux sans fil et techniques associées ...................................................

We present and analyse in this paper a novel colocated Finite Volume scheme for the solution of the Stokes problem. It has been developed following two main ideas. On one hand, the discretization of the pressure gradient term is built as the discrete transposed of the velocity divergence term, the latter being evaluated using a natural finite volume approximation; this leads to a nonstandard in...

We survey work on stability and smoothing estimates in maximum-norm for spatially semidiscrete finite element approximations of a model parabolic equation, and related such estimates for the resolvent of the corresponding discrete elliptic operator. We end with a short discussion of stability of fully discrete time stepping methods. Résumé. Nous présentons un bilan des résultats sur la stabilit...