Stability and error analysis of a splitting method using Robin-Robin coupling applied to a fluid-structure interaction problem

Abstract: We analyze a splitting method for a canonical fluid structure interaction problem. The splittling method uses a Robin-Robin boundary condition, explicit strategy. We prove the method is stable and, furthermore, we provide an error estimate that shows the error at the final time $T$ is $O(\sqrt{T\Delta t})$ where $\Delta t$ is the time step.