  We present a complete numerical analysis for a general discretization of a
coupled flow-mechanics model in fractured porous media, considering
single-phase flows and including frictionless contact at matrix-fracture
interfaces, as well as nonlinear poromechanical coupling. Fractures are
described as planar surfaces, yielding the so-called mixed- or
hybrid-dimensional models. Small displacements and a linear elastic behavior
are considered for the matrix. The model accounts for discontinuous fluid
pressures at matrix-fracture interfaces in order to cover a wide range of
normal fracture conductivities. The numerical analysis is carried out in the
Gradient Discretization framework, encompassing a large family of conforming
and nonconforming discretizations. The convergence result also yields, as a
by-product, the existence of a weak solution to the continuous model. A
numerical experiment in 2D is presented to support the obtained result,
employing a Hybrid Finite Volume scheme for the flow and second-order finite
elements ($\mathbb P_2$) for the mechanical displacement coupled with face-wise
constant ($\mathbb P_0$) Lagrange multipliers on fractures, representing normal
stresses, to discretize the contact conditions.
