Twofold saddle-point formulation of Biot poroelasticity with stress-dependent diffusion

Abstract

We introduce a stress/total-pressure formulation for poroelasticity that includes the coupling with steady nonlinear diffusion modified by stress. The nonlinear problem is written in mixed-primal form, coupling a perturbed twofold saddle-point system with an elliptic problem. The continuous formulation is analysed in the framework of abstract fixed-point theory and Fredholm alternative for compact operators. A mixed finite element method is proposed and its stability and convergence analysis are carried out. We also include a few illustrative numerical tests. The resulting model can be used to study waste removal in the brain parenchyma, where diffusion of a tracer alone or a combination of advection and diffusion are not sufficient to explain the alterations in rates of filtration observed in porous media samples.

References in corpus (4)

• The Biot-Stokes coupling using total pressure: formulation, analysis and application to interfacial flow in the eye
• A coupled multipoint stress -- multipoint flux mixed finite element method for the Biot system of poroelasticity
• Fast uncertainty quantification of tracer distribution in the brain interstitial fluid with multilevel and quasi Monte Carlo
• Coupling Stokes flow with inhomogeneous poroelasticity

Cited by in corpus (2)

• New twofold saddle-point formulations for Biot poroelasticity with porosity-dependent permeability
• Robust virtual element methods for coupled stress-assisted diffusion problems