Decoupling multistep schemes for elliptic-parabolic problems
Abstract
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.
Cite
@article{arxiv.2407.18594,
title = {Decoupling multistep schemes for elliptic-parabolic problems},
author = {Robert Altmann and Abdullah Mujahid and Benjamin Unger},
journal= {arXiv preprint arXiv:2407.18594},
year = {2025}
}