Robust Discretization of Flow in Fractured Porous Media

Abstract

Flow in fractured porous media represent a challenge for discretization methods due to the disparate scales and complex geometry. Herein we propose a new discretization, based on the mixed finite element method and mortar methods. Our discretization handles complex, non-matching grids, and allows for fracture intersections and termination in a natural way. The discretization is applicable to both two and three spatial dimensions. Furthermore, we show how to obtain a finite volume variant in terms of cell-center pressures. Analysis shows the method to be first order convergent, which is sustained by the numerical examples.