Linear poroelasticity with solid incompressibility: consistent formulation and scalable numerical solution

In this work we propose, by linearizing the equations of fully nonlinear poroelasticity, a consistent model in which only the solid phase is incompressible. This reformulation circumvents some inconsistency issues encountered in standard primal formulations of nonlinear poroelasticity while still retaining its key physical coupling mechanisms. We show a well-posed and consistent discretization strategy and also formulate scalable solvers based on a Schur complement formalism. A distinctive feature of the model is that it allows for a lowest order, inf-sup stable family of Finite Elements (FE) spaces. Numerical tests in two and three dimensions are provided to validate the proposed method and solver framework.