When developing a numerical method for a coupled system, improper treatment of coupling conditions can result in critical issues, particularly with regards to the stability of the method. Examples include the well-known added-mass instability for fluid-structure interaction (FSI) problems modeling fluid flow interacting with an elastic solid. In this talk, we explore the use of Robin-type interface conditions to develop loosely coupled time-splitting methods for multiphysics systems. Assuming negligible deformations of the interface, this method has been proven to be unconditionally stable with quasi-optimal error estimates in time. We will focus primarily on the application of these methods to the FSI problem, however, we will also discuss their applicability to more general classes of coupled problems. Critically, the values of the physical parameters do not impact the stability, so the splitting method does not suffer from the added-mass instability that is common to other loosely coupled methods. 

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