  In this paper, we are interested in an efficient numerical method for the
mixed-dimensional approach to modeling single-phase flow in fractured porous
media. The model introduces fractures and their intersections as
lower-dimensional structures, and the mortar variable is used for flow coupling
between the matrix and fractures. We consider a stable mixed finite element
discretization of the problem, which results in a parameter-dependent linear
system. For this, we develop block preconditioners based on the well-posedness
of the discretization choice. The preconditioned iterative method demonstrates
robustness with regards to discretization and physical parameters. The
analytical results are verified on several examples of fracture network
configurations, and notable results in reduction of number of iterations and
computational time are obtained.
