Higher-order iterative decoupling for poroelasticity
Numerical Analysis
2026-05-25 v2 Numerical Analysis
Abstract
For the iterative decoupling of elliptic-parabolic problems such as poroelasticity, we introduce time discretization schemes up to order based on the backward differentiation formulae. Its analysis combines techniques known from fixed-point iterations with the convergence analysis of the temporal discretization. As main result, we show that the convergence depends on the interplay between the time step size and the parameters for the contraction of the iterative scheme. Moreover, this connection is quantified explicitly, which allows for balancing the single error components. Several numerical experiments illustrate and validate the theoretical results, including a three-dimensional example from biomechanics.
Cite
@article{arxiv.2311.14400,
title = {Higher-order iterative decoupling for poroelasticity},
author = {Robert Altmann and Abdullah Mujahid and Benjamin Unger},
journal= {arXiv preprint arXiv:2311.14400},
year = {2026}
}