Well-posedness and discrete analysis for advection-diffusion-reaction in poroelastic media

We analyse a PDE system modelling poromechanical processes (formulated in mixed form using the solid deformation, fluid pressure, and total pressure) interacting with diffusing reacting solutes medium. investigate well-posedness of nonlinear set equations fixed-point theory, Fredholm's alternative, priori estimates, compactness arguments. also propose finite element method rigorously demonstrate stability scheme. Error estimates are derived suitable norms, numerical experiments conducted to illustrate mechano-chemical coupling verify theoretical rates convergence.