A Three-Field Formulation for Poroelasticity

In this talk we present a stable and convergent conforming finite element method for the discretisation of the linear poroelasticity equations in a new formulation, where the volumetric contributions to the total stress are merged into an additional unknown. The resulting saddle point formulation can be analysed by means of a Fredholm alternative, after realizing that the problem is a compact perturbation of a Stokes-like invertible system. A generic Galerkin scheme is constructed, whose solvability properties follow closely those from the continuous variational form, and more importantly, given that specific finite dimensional spaces are chosen adequately, it is stable even in the incompressible limit. Contatto: luca.formaggia@polimi.it