Nonlinear Darcy fluid flow with deposition

In this article we consider a model of a filtration process. The process is modeled using the nonlinear Darcy fluid flow equations with a varying permeability, coupled with a deposition equation. Existence and uniqueness of the solution to the modeling equations is established. A numerical approximation scheme is proposed and analyzed, with an a priori error estimate derived. Numerical experiments are presented which support the obtained theoretical results.