Towards an inf-sup theory for the Biot equations in poroelasticity
A talk in the BI.discrete Workshop series by
Pietro Zanotti from Pavia
| Abstract: | In the theory of poroelasticity, the 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 explicit 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 this direction. More precisely, we discuss a possible application of the inf-sup theory after a time semi-discretization of the Biot equations with the backward Euler scheme. We propose a space discretization inspired by our findings and we discuss the a priori error analysis. This is a joint work with A. Khan.
Within the CRC this talk is associated to the project(s): B7 |