A Reduced Basis Method for a PDE-constrained optimization formulation in Discrete Fracture Network flow simulations

In classic Reduced Basis (RB) framework, we propose a new technique for the offline greedy error analysis which relies on a residual-based a posteriori error estimator. This approach is as an alternative to classical a posteriori RB estimators, avoiding a discrete inf-sup lower bound estimate. We try to use less common ingredients of the RB framework to retrieve a better approximation of the RB error, such as the estimation of the distance between the continuous solution and the reduced one. In particular we focus on the application of the reduction model for the flow simulations in underground fractured media, in which high accurate simulations suffer for the complexity of the domain geometry. Finally, some numerical tests are assessed to confirm the viability and the efficacy of the technique proposed.