  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.
