  In this paper, we develop a discretization for the non-linear coupled model
of classical Darcy-Forchheimer flow in deformable porous media, an extension of
the quasi-static Biot equations. The continuous model exhibits a generalized
gradient flow structure, identifying the dissipative character of the physical
system. The considered mixed finite element discretization is compatible with
this structure, which gives access to a simple proof for the existence,
uniqueness, and stability of discrete approximations. Moreover, still within
the framework, the discretization allows for the development of finite volume
type discretizations by lumping or numerical quadrature, reducing the
computational cost of the numerical solution.
