Adaptive mixed finite element methods for Darcy flow in fractured porous media. Issue 10 (12th October 2016) - Chen, Huangxin; Salama, Amgad; Sun, Shuyu
Abstract: In this paper, we propose adaptive mixed finite element methods for simulating the single‐phase Darcy flow in two‐dimensional fractured porous media. The reduced model that we use for the simulation is a discrete fracture model coupling Darcy flows in the matrix and the fractures, and the fractures are modeled by one‐dimensional entities. The Raviart‐Thomas mixed finite element methods are utilized for the solution of the coupled Darcy flows in the matrix and the fractures. In order to improve the efficiency of the simulation, we use adaptive mixed finite element methods based on novel residual‐based a posteriori error estimators. In addition, we develop an efficient upscaling algorithm to compute the effective permeability of the fractured porous media. Several interesting examples of Darcy flow in the fractured porous media are presented to demonstrate the robustness of the algorithm. Key Points: Adaptive mixed finite element method is proposed for simulation of Darcy flow in fractured porous media A novel residual type of a posteriori error estimator is introduced An efficient upscaling algorithm is proposed to compute the effective permeability of the fractured porous media