Convergent adaptive iterative schemes for solving multi-physics problems
Numerical Analysis
2026-01-26 v1 Numerical Analysis
Abstract
In this paper, we derive a practical, general framework for creating adaptive iterative (linearization or splitting) algorithms to solve multi-physics problems. This means that, given an iterative method, we derive \textit{a posteriori} estimators to predict the success or failure of the method. Based on these estimators, we propose adaptive algorithms, including adaptively switching between methods, adaptive time-stepping methods, and the adaptive tuning of stabilization parameters. We apply this framework to two-phase flow in porous media, surfactant transport in porous media, and quasi-static poroelasticity.
Cite
@article{arxiv.2601.16640,
title = {Convergent adaptive iterative schemes for solving multi-physics problems},
author = {Jakob S. Stokke and Kundan Kumar and Florin A. Radu},
journal= {arXiv preprint arXiv:2601.16640},
year = {2026}
}