On Simulations of Discrete Fracture Network Flows with an Optimization-Based Extended Finite Element Method

Following the approach introduced in [SIAM J. Sci. Comput., 35 (2013), pp. B487– B510], we consider the formulation of the problem of fluid flow in a system of fractures as a PDE constrained optimization problem, with discretization performed using suitable extended finite elements; the method allows independent meshes on each fracture, thus completely circumventing meshing problems usually related to the discrete fracture network (DFN) approach. The application of the method to DFNs of medium complexity is fully analyzed here, accounting for several issues related to viable and reliable implementations of the method in complex problems.