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.

在经典的缩减基础 (RB) 框架中，我们提出了一种离线贪婪误差分析的新技术，该技术依赖于基于残差的后验误差估计器。这种方法可以替代经典的后验 RB 估计量，避免离散 inf-sup 下限估计。我们尝试使用 RB 框架中不太常见的成分来检索 RB 误差的更好近似值，例如估计连续解与缩减解之间的距离。特别是我们专注于减少模型在地下裂隙介质中的流动模拟的应用，其中高精度模拟受到域几何复杂性的影响。最后，对一些数值测试进行了评估，以确认所提出技术的可行性和有效性。