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

Abstract

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