Abstract: In this talk an adaptive mixed finite element method will be introduced for the Darcy flow in a two-dimensional fractured porous media. The discrete fracture model (DFM) is applied to model the fractures by one-dimensional fractures in a two-dimensional domain. We derive a robust residual-based a posteriori error estimator for the problem with non-intersecting fractures. Then applying the adaptive algorithm, we will further introduce an efficient upscaling algorithm to compute the effective permeability of the fractured porous media, and a two-scale reduced model for simulating the flow in the porous media with conductive fractures. Several numerical results will be shown to demonstrate the efficiency of the adaptive algorithm and the proposed two-scale model.
Bio: Dr. Chen received his Ph.D. from AMSS, Chinese Academy of Sciences in 2011. Then he joined in the School of Mathematical Sciences of Xiamen University in 2011 and now he is an Associate Professor in Xiamen University. He also worked as a postdoc at KAUST during the period from May 2015 to February 2016. His research interests include adaptive finite element methods, multigrid methods, discontinuous Galerkin method, and flow and transport in porous media. His recent work focuses on the simulation of flow and transport problems in fractured porous media and the related topics in the field of petroleum reservoir simulation.