Numerical approximation for hybrid‐dimensional flow and transport in fractured porous media

Abstract This article presents the stable miscible displacement problem in fractured porous media, and finite element discretization is constructed for this reduced model. The transmission interface conditions presented in this article enable us to derive a stability result and conduct the case where the pressure and concentration are both discontinuous across the fracture. The error estimates for and norm are established under the assumption of regular solutions. We perform some numerical examples to verify the theoretical analysis. Last, some unsteady physical experiments, more realistic test cases, are presented to prove the validity of the model and method.