AN ADAPTIVE DISCONTINUOUS GALERKIN METHOD FOR A STOKES/BIOT
FLUID-POROELASTIC STRUCTURE INTERACTION MODEL
The paper presents an a posteriori error estimator for a (piecewise
linear) nonconforming finite element approximation 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. The
approach utilizes the same nonconforming Crouzeix-Raviart element
discretization on the entire domain [Houédanou Koffi Wilfrid, Results
in Applied Mathematics 7 (2020) 100127, Elsevier]. For this
discretization, we derive a residual indicator based on the jumps of
normal derivative of the nonconforming approximation. Lower and upper
bounds form the main results with minimal assumptions on the mesh.