Splitting methods for coupled problems based on Robin-Robin coupling conditions

We develop a loosely coupled splitting method for coupled problems called the Robin-Robin splitting method based on Robin-type interface conditions. We apply this method to several coupled problems, most notably the fluid-structure interaction problem in both a time-semi-discrete framework and a fully discrete framework.
We demonstrate that the method is unconditionally stable and that the error also decreases nearly optimally, although this behavior can be significantly delayed depending on the values of the physical parameters in the fluid-structure interaction problem. Critically, as the Robin-Robin method is unconditionally stable in time, it does not suffer from the added-mass instability known to pose an issue for other loosely coupled splitting methods applied to the fluid-structure interaction problem.