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arXiv · 2407.18594

Decoupling multistep schemes for elliptic-parabolic problems

Robert Altmann·Abdullah Mujahid·Benjamin Unger
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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.

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Robert Altmann, Abdullah Mujahid, Benjamin Unger. 2024-07-26. Decoupling multistep schemes for elliptic-parabolic problems. https://arxiv.org/abs/2407.18594

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