Fluid-structure partitioned procedures based on Robin transmission conditions

In this article we design new partitioned procedures for fluid-structure interaction problems, based on Robin-type transmission conditions. The choice of the coefficient in the Robin conditions is justified via simplified models.
The strategy is effective whenever an incompressible fluid interacts with a relatively thin membrane, as in hemodynamics applications.
We analyze theoretically the new iterative procedures on a model problem, which represents a simplified blood-vessel system.
In particular, the Robin-Neumann scheme exhibits enhanced convergence properties with respect to the existing partitioned procedures. The theoretical results are checked using numerical experimentation.