Mortar finite element discretization of the time dependent nonlinear Darcy's equations

We consider the non stationary flow of a viscous incompressible fluid in a rigid homogeneous porous medium provided with mixed boundary conditions. Since the medium is nonhomogeneous, its permeability is only piecewise continuous. We are thus led to use the mortar method to handle these discontinuities. We propose a space and time discretization of the full system. We prove optimal a priori error estimates, which confirms the interest of the discretization.