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

Erik Burman (1) , Rebecca Durst (2) , Miguel Angel Fernández (3) , Johnny Guzmán (2)

1 UCL London - Department of Mathematics
2 Brown University
3 COMMEDIA - COmputational Mathematics for bio-MEDIcal Applications

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(∆(T + log(1/∆t))^1/2), where ∆t is the time step.

Mots clés: Loosely coupled scheme; Robin-Robin scheme; parabolic-hyperbolic coupling.

Domaines: Analyse numérique [math.NA]

Erik Burman, Rebecca Durst, Miguel Angel Fernández, Johnny Guzmán. Loosely coupled, non-iterative time-splitting scheme based on Robin-Robin coupling: Unified analysis for Parabolic/Parabolic and Parabolic/Hyperbolic problems. Journal of Numerical Mathematics, 2023, 31 (1), pp.59-77. ⟨10.1515/jnma-2021-0119⟩. ⟨hal-03381765⟩