Reliable a posteriori mesh adaptivity in discrete fracture network flow simulations

A new approach for the flow simulation in very complex Discrete Fracture Networks (DFNs) based on PDE-constrained optimization has been recently proposed in Berrone et al. (2013, 2014) with the aim of improving robustness with respect to geometrical complexities. In Berrone et al. (2016) a rigorous derivation of “a posteriori” error estimates has been performed, proving an equivalence relation between the discretization error and suitable quantities that are computable from the discrete solution and the problem data. In this paper, the previous results are applied to several fracture networks in order to investigate mesh adaptivity applied to complex realistic fracture networks