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arXiv · 2110.08181

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

Erik Burman·Rebecca Durst·Miguel Fernández·Johnny Guzmán
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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

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Erik Burman, Rebecca Durst, Miguel Fernández, Johnny Guzmán. 2021-10-15. Loosely coupled, non-iterative time-splitting scheme based on Robin-Robin coupling: unified analysis for parabolic/parabolic and parabolic/hyperbolic problems. https://arxiv.org/abs/2110.08181

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