A second-order correction method for loosely coupled discretizations applied to parabolic-parabolic interface problems
<|reference_start|>A second-order correction method for loosely coupled discretizations applied to parabolic-parabolic interface problems: We consider a parabolic-parabolic interface problem and construct a loosely coupled prediction-correction scheme based on the Robin-Robin splitting method analyzed in [J. Numer. Math., 31(1):59--77, 2023]. We show that the errors of the correction step converge at $\mathcal O((\Delta t)^2)$, under suitable convergence rate assumptions on the discrete time derivative of the prediction step, where $\Delta t$ stands for the time-step length. Numerical results are shown to support our analysis and the assumptions.<|reference_end|>
@article{burman2024a,
    title={A second-order correction method for loosely coupled discretizations
  applied to parabolic-parabolic interface problems},
    author={Erik Burman, Rebecca Durst, Miguel A. Fern'andez, Johnny Guzm'an,
  Sijing Liu},
    journal={arXiv preprint arXiv:2404.01599},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.01599},
    primaryClass={math.NA cs.NA}
}