Decoupling multistep schemes for elliptic-parabolic problems
<|reference_start|>Decoupling multistep schemes for elliptic-parabolic problems: We study the construction and convergence of decoupling multistep schemes of higher order using the backward differentiation formulae for an elliptic-parabolic problem, which includes multiple-network poroelasticity as a special case. These schemes were first introduced in [Altmann, Maier, Unger, BIT Numer. Math., 64:20, 2024], where a convergence proof for the second-order case is presented. Here, we present a slightly modified version of these schemes using a different construction of related time delay systems. We present a novel convergence proof relying on concepts from G-stability applicable for any order and providing a sharper characterization of the required weak coupling condition. The key tool for the convergence analysis is the construction of a weighted norm enabling a telescoping argument for the sum of the errors.<|reference_end|>
@article{altmann2024decoupling,
    title={Decoupling multistep schemes for elliptic-parabolic problems},
    author={Robert Altmann and Abdullah Mujahid and Benjamin Unger},
    journal={arXiv preprint arXiv:2407.18594},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.18594},
    primaryClass={math.NA cs.NA}
}