We are interested in the discretization of parabolic equations, either linear or semilinear, by an implicit Euler scheme with respect to the time variable and finite elements with respect to the space variables. The main result of this paper consists of building error indicators with respect to both time and space approximations and proving their equivalence with the error, in order to work wit...

The aim of this paper is to show that, for a linear second-order hyperbolic equation discretized by the backward Euler scheme in time and continuous piecewise linear finite elements in space, the adaptation of the time steps can be combined with spatial mesh adaptivity in an optimal way. We derive a priori and a posteriori error estimates which admit, as much as it is possible, the decoupling o...

RÉSUMÉ. Les méthodes permettant de mesurer la proximité dans un espace métrique ont trouvé de nouvelles applications récentes avec la recherche sur Internet. Nous présentons ici une nouvelle approche pour la recherche sur Internet. Nous utilisons une combinaison des mesures de distance dans un espace métrique et l’analyse des liens pour définir la proximité des objets sur Internet. Cette struct...

We compare the block-Lanczos and the Davidson methods for computing a basis of a singular subspace associated with the smallest singular values of large matrices. We introduce a simple modiication on the preconditioning step of Davidson's method which appears to be eecient on a range of large sparse matrices. Calcul du sous espace singulier associ e aux plus petites valeurs singuli eres de matr...