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

TL;DR

This paper introduces a stable, non-iterative time-splitting scheme using Robin-Robin coupling for parabolic and hyperbolic systems, with proven error convergence and unified analysis.

Contribution

It proposes a novel, unified analysis of a loosely coupled Robin-Robin scheme applicable to both parabolic/parabolic and parabolic/hyperbolic problems, demonstrating stability and convergence.

Findings

Scheme is stable for both systems

Error converges at a rate involving Δt and logarithmic factors

Unified analysis applies to multiple coupled systems

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 $\mathcal{O}\big(\Delta t \sqrt{T +\log{\frac{1}{\Delta t}}}\big)$, where $\Delta t$ is the time step