Titre : Towards an inf-sup theory for the Biot equations in poroelasticity
Résumé : In the theory of poroelasticity, the quasi-static Biot equations model the flow of a fluid inside a linear elastic porous medium. The equations have been previously analyzed by energy arguments, following the Faedo-Galerkin scheme, or via the operator theory. We are interested in a new approach, based on the Banach-Necas theorem, i.e. on the so-called inf-sup theory. The proposed approach, when successful, establishes an isomorphism between the spaces of the data and of the solutions and this, in turn, is an important device in the derivation of sharp a priori and a posteriori error estimates for a discretization of the equations. We illustrate some preliminary results obtained in direction. This is a joint work with A. Khan and C. Kreuzer.
