Mathematical modelling and numerical approximation of a leachate flow in the anaerobic biodegradation of waste in a landfill

We consider a coupled PDE–ODE model governing the bacterial dynamics of anaerobic biodegradation household waste in landfill. The biological activity, represented with non linear system ordinary differential equations (ODE), takes place an unsaturated porous medium by Darcy law. transform initial into fully PDE where distribution is spatialized as reaction–diffusion equations. carry out mathematical and numerical analysis new its discrete counterpart variational framework. Using mixed finite elements approximation for nonlinear flow standard to solve system, we perform several simulations 2D 3D agreement theoretical results.