Luis Miguel De Oliveira Vilaca, Bryan Gomez-Vargas, Sarvesh Kumar, Ricardo Ruiz-Baier, Nitesh Verma:
Advection-diffusion-reaction in poroelastic media. Part I: Well-posedness and discrete analysis
We analyse a PDE system modelling poromechanical processes (formulated in mixed form using the solid deformation, fluid pressure, and total pressure) interacting with diffusing and reacting solutes in the medium. We investigate the well-posedness of the nonlinear set of equations using fixed-point theory, Fredholm’s alternative, a priori estimates, and compactness arguments. We also propose a mixed finite element method and rigorously demonstrate the stability of the scheme.