Biot-Stokes modeling of flow in fractured poroelastic media Ivan Yotov University of Pittsburgh We study mathematical models and their finite element approximations for solving the coupled problem arising in the interaction between fluid in a poroelastic material and fluid in a fracture. The fluid flow in the fracture is governed by the Stokes/Brinkman equations, while the poroelastic material is modeled using the Biot system. We present several approaches to impose the continuity of normal flux, including an interior penalty method and a Lagrange multiplier method. A dimensionally reduced fracture model based on averaging the equations over the cross-sections will also be presented. Stability, accuracy, and robustness of the methods will be discussed.