Stokes-Biot Modeling of Flow in Fractured Poroelastic Media

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.