Mixed-Hybrid FEM Discrete Fracture Network Model of the Fracture Flow

We consider a steady saturated Darcy's-law-govemed flow of an incompressible fluid through a system of 2D polygons embedded in 3D space and connected under certain conditions into one network. This may simulate underground water flow through natural geological disruptions of a rock massif, fractures, e.g., for the purposes of finding suitable nuclear waste repositories. Note that an intersection of three or more triangles through one edge in the discretization is possible owing to the special geometrical situation (see Fig. 1). We study the existence and uniqueness of weak and discrete mixed solutions, and finally use the hybridization of the lowest order Raviart-Thomas mixed approximation (see [3,4] respectively). For the technical details of what follows, see [5].