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

TL;DR

This paper analyzes a Robin-Robin splitting method for fluid-structure interaction, proving its stability and providing an error estimate that scales with the square root of the final time and time step.

Contribution

The paper introduces and rigorously analyzes a Robin-Robin boundary condition-based splitting method, establishing stability and deriving an explicit error bound.

Findings

The method is proven to be stable.

An error estimate of O(√(TΔt)) is derived.

The approach is explicit and applicable to fluid-structure interaction problems.

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.