  We present a hybrid-mixed finite element method for
  a novel hybrid-dimensional model of single-phase Darcy flow in a fractured
porous media. In this model, the fracture is treated as an $(d-1)$-dimensional
interface within the $d$-dimensional fractured porous domain, for $d=2, 3$. Two
classes of fracture are distinguished based on the permeability magnitude ratio
between the fracture and its surrounding medium: when the permeability in the
fracture is (significantly) larger than in its surrounding medium, it is
considered as a {\it conductive} fracture; when the permeability in the
fracture is (significantly) smaller than in its surrounding medium, it is
considered as a {\it blocking} fracture. The conductive fractures are treated
using the classical hybrid-dimensional approach of the interface model where
pressure is assumed to be continuous across the fracture interfaces, while the
blocking fractures are treated using the recent Dirac-$\delta$ function
approach where normal component of Darcy velocity is assumed to be continuous
across the interface. Due to the use of Dirac-$\delta$ function approach for
the blocking fractures, our numerical scheme allows for nonconforming meshes
with respect to the blocking fractures. This is the major novelty of our model
and numerical discretization. Moreover, our numerical scheme produces locally
conservative velocity approximations and leads to a symmetric positive definite
linear system involving pressure degrees of freedom on the mesh skeleton only.
The performance of the proposed method is demonstrated by various benchmark
test cases in both two- and three-dimensions. Numerical results indicate that
the proposed scheme is highly competitive with existing methods in the
literature.
