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We investigate the discretization of Darcy flow through fractured porousmedia on general meshes. We consider a hybrid dimensional model, invoking acomplex network of planar fractures. The model accounts for matrix-fractureinteractions and fractures acting either as drains or as barriers, i.e. we haveto deal with pressure discontinuities at matrix-fracture interfaces. Thenumerical analysis is performed in the general framework of gradientdiscretizations which is extended to the model under consideration. Twofamilies of schemes namely the Vertex Approximate Gradient scheme (VAG) and theHybrid Finite Volume scheme (HFV) are detailed and shown to satisfy thegradient scheme framework, which yields, in particular, convergence. Numericaltests confirm the theoretical results. Gradient Discretization; Darcy Flow,Discrete Fracture Networks, Finite Volume

Gradient discretization of Hybrid Dimensional Darcy Flows in Fractured Porous Media with discontinuous pressures at the matrix fracture interfaces