  We investigate the discretization of Darcy flow through fractured porous
media on general meshes. We consider a hybrid dimensional model, invoking a
complex network of planar fractures. The model accounts for matrix-fracture
interactions and fractures acting either as drains or as barriers, i.e. we have
to deal with pressure discontinuities at matrix-fracture interfaces. The
numerical analysis is performed in the general framework of gradient
discretizations which is extended to the model under consideration. Two
families of schemes namely the Vertex Approximate Gradient scheme (VAG) and the
Hybrid Finite Volume scheme (HFV) are detailed and shown to satisfy the
gradient scheme framework, which yields, in particular, convergence. Numerical
tests confirm the theoretical results. Gradient Discretization; Darcy Flow,
Discrete Fracture Networks, Finite Volume
