Twofold Saddle-Point Formulation of Biot Poroelasticity with Stress-Dependent Diffusion

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