Weak Galerkin Finite Element Methods for the Simulation of Single-Phase Flow in Fractured Porous Media

This paper presents a numerical simulation of the flow in fractured porous media, which can be efficiently described by the reduced model consisting of the bulk problem in the porous matrix and the fracture problem in the fracture together with physically consistent coupling conditions. The reduced model is solved by using two types of weak Galerkin finite element methods (on simplex mesh and polygonal mesh, respectively) for the bulk problem coupled with the cell centered finite volume method for the fracture problem. We prove that the algebraic system arising in the discrete formulation is symmetric and positive-definite, which leads to the well-posedness of the discrete problem. Error estimates for the pressure in suitable norms are established. A series of numerical experiments demonstrate the accuracy and robustness of our method with respect to the shape of the grid and the permeability of the fractures.