Loosely coupled, non-iterative time-splitting scheme based on Robin-Robin coupling: unified analysis for parabolic/parabolic and parabolic/hyperbolic problems

Abstract

We present a loosely coupled, non-iterative time-splitting scheme based on Robin-Robin coupling conditions. We apply a novel unified analysis for this scheme applied to both a Parabolic/Parabolic coupled system and a Parabolic/Hyperbolic coupled system. We show for both systems that the scheme is stable, and the error converges as $\mathcal{O}\left(\Delta t\sqrt{T+\log \frac{1}{\Delta t}}\right)$, where $\Delta t$ is the time step