Convergent adaptive iterative schemes for solving multi-physics problems
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866915750186319872 |
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| author | Stokke, Jakob S. Kumar, Kundan Radu, Florin A. |
| author_facet | Stokke, Jakob S. Kumar, Kundan Radu, Florin A. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_16640 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Convergent adaptive iterative schemes for solving multi-physics problems Stokke, Jakob S. Kumar, Kundan Radu, Florin A. Numerical Analysis 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. |
| title | Convergent adaptive iterative schemes for solving multi-physics problems |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2601.16640 |