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On the convergence rate of the Kačanov scheme for shear-thinning fluids
We explore the convergence rate of the Kačanov iteration scheme for different models of shear-thinning fluids, including Carreau and power-law type explicit quasi-Newtonian constitutive laws. It is shown that the energy difference contracts along the sequence generated by the iteration. In addition,...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Springer International Publishing
2021
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8627928/ https://www.ncbi.nlm.nih.gov/pubmed/34898682 http://dx.doi.org/10.1007/s10092-021-00444-3 |
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author | Heid, Pascal Süli, Endre |
author_facet | Heid, Pascal Süli, Endre |
author_sort | Heid, Pascal |
collection | PubMed |
description | We explore the convergence rate of the Kačanov iteration scheme for different models of shear-thinning fluids, including Carreau and power-law type explicit quasi-Newtonian constitutive laws. It is shown that the energy difference contracts along the sequence generated by the iteration. In addition, an a posteriori computable contraction factor is proposed, which improves, on finite-dimensional Galerkin spaces, previously derived bounds on the contraction factor in the context of the power-law model. Significantly, this factor is shown to be independent of the choice of the cut-off parameters whose use was proposed in the literature for the Kačanov iteration applied to the power-law model. Our analytical findings are confirmed by a series of numerical experiments. |
format | Online Article Text |
id | pubmed-8627928 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2021 |
publisher | Springer International Publishing |
record_format | MEDLINE/PubMed |
spelling | pubmed-86279282021-12-10 On the convergence rate of the Kačanov scheme for shear-thinning fluids Heid, Pascal Süli, Endre Calcolo Article We explore the convergence rate of the Kačanov iteration scheme for different models of shear-thinning fluids, including Carreau and power-law type explicit quasi-Newtonian constitutive laws. It is shown that the energy difference contracts along the sequence generated by the iteration. In addition, an a posteriori computable contraction factor is proposed, which improves, on finite-dimensional Galerkin spaces, previously derived bounds on the contraction factor in the context of the power-law model. Significantly, this factor is shown to be independent of the choice of the cut-off parameters whose use was proposed in the literature for the Kačanov iteration applied to the power-law model. Our analytical findings are confirmed by a series of numerical experiments. Springer International Publishing 2021-11-28 2022 /pmc/articles/PMC8627928/ /pubmed/34898682 http://dx.doi.org/10.1007/s10092-021-00444-3 Text en © The Author(s) 2021 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) . |
spellingShingle | Article Heid, Pascal Süli, Endre On the convergence rate of the Kačanov scheme for shear-thinning fluids |
title | On the convergence rate of the Kačanov scheme for shear-thinning fluids |
title_full | On the convergence rate of the Kačanov scheme for shear-thinning fluids |
title_fullStr | On the convergence rate of the Kačanov scheme for shear-thinning fluids |
title_full_unstemmed | On the convergence rate of the Kačanov scheme for shear-thinning fluids |
title_short | On the convergence rate of the Kačanov scheme for shear-thinning fluids |
title_sort | on the convergence rate of the kačanov scheme for shear-thinning fluids |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8627928/ https://www.ncbi.nlm.nih.gov/pubmed/34898682 http://dx.doi.org/10.1007/s10092-021-00444-3 |
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