Nonconforming finite element methods for a Stokes/Biot fluid–poroelastic structure interaction model

Abstract

We analyze a strongly coupled mixed formulation of the problem defining the interaction between a free fluid and poroelastic structure. The free fluid is governed by the Stokes equations, while the flow in the poroelastic medium is modeled using the Biot poroelasticity system. Equilibrium and kinematic conditions are imposed on the interface. A stabilized mixed finite element method for solving the stationary coupled Stokes–Biot flows problem is formulated and analyzed. The approach utilizes the same nonconforming Crouzeix–Raviart (C–R) element discretization on the entire domain. Under a small data assumption, existence and uniqueness results are proved and an optimal a priori error estimate is derived.

Keywords

• Stokes–Biot model
• Nonconforming finite element method
• A priori error analysis