The schematic of the Embedded Discrete Fracture Model (EDFM). The red points represent the matrix grids, which storage fluid pressure; the blue points denote the fracture grids, which storage fracture pressure and displacement for the XFVM; the bright green points storage the matrix displacement for the XFVM and XFEM; e, w, n, s represent the interface of control volume; E, W, N, S represent the internal interface in a control volume.