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New highly efficient and accurate numerical scheme for the Cahn-Hilliard-Brinkman system.

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Title: New highly efficient and accurate numerical scheme for the Cahn-Hilliard-Brinkman system.
Authors: Chen, Dawei1 (AUTHOR) cdwstnu@163.com, Ren, Qinzhen1 (AUTHOR) qzhen2017@163.com, Li, Minghui1 (AUTHOR) minghuili_xmu@163.com
Source: Computers & Mathematics with Applications. Feb2026, Vol. 204, p182-197. 16p.
Subjects: Relaxation methods (Mathematics), Numerical analysis, Cahn-Hilliard-Cook equation, Simulation methods & models, Iterative methods (Mathematics), Stability of linear systems
Abstract: In this paper, based on a generalized scalar auxiliary variable approach with relaxation (R-GSAV), we construct a class of high-order backward differentiation formula (BDF) schemes with variable time steps for the Cahn-Hilliard-Brinkman(CHB) system. In theory, it is strictly proved that the designed schemes are unconditionally energy-stable. With the delicate treatment of adaptive strategies, we propose several adaptive time-stepping algorithms to enhance the robustness of the schemes. More importantly, a novel hybrid-order adaptive time steps algorithm performs outstanding for the coupled system. The hybrid-order algorithm inherits the advantages of some traditional high-order BDF adaptive strategies. A comprehensive comparison with some adaptive time-stepping algorithms is given, and the advantages of the new adaptive time-stepping algorithms are emphasized. Finally, the effectiveness and accuracy of the new methods are validated through a series of numerical experiments. [ABSTRACT FROM AUTHOR]
Copyright of Computers & Mathematics with Applications is the property of Pergamon Press - An Imprint of Elsevier Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
An: 191324171
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  Data: New highly efficient and accurate numerical scheme for the Cahn-Hilliard-Brinkman system.
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  Data: <searchLink fieldCode="AR" term="%22Chen%2C+Dawei%22">Chen, Dawei</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> cdwstnu@163.com</i><br /><searchLink fieldCode="AR" term="%22Ren%2C+Qinzhen%22">Ren, Qinzhen</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> qzhen2017@163.com</i><br /><searchLink fieldCode="AR" term="%22Li%2C+Minghui%22">Li, Minghui</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> minghuili_xmu@163.com</i>
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  Data: <searchLink fieldCode="JN" term="%22Computers+%26+Mathematics+with+Applications%22">Computers & Mathematics with Applications</searchLink>. Feb2026, Vol. 204, p182-197. 16p.
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  Data: <searchLink fieldCode="DE" term="%22Relaxation+methods+%28Mathematics%29%22">Relaxation methods (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Cahn-Hilliard-Cook+equation%22">Cahn-Hilliard-Cook equation</searchLink><br /><searchLink fieldCode="DE" term="%22Simulation+methods+%26+models%22">Simulation methods & models</searchLink><br /><searchLink fieldCode="DE" term="%22Iterative+methods+%28Mathematics%29%22">Iterative methods (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Stability+of+linear+systems%22">Stability of linear systems</searchLink>
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  Label: Abstract
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  Data: In this paper, based on a generalized scalar auxiliary variable approach with relaxation (R-GSAV), we construct a class of high-order backward differentiation formula (BDF) schemes with variable time steps for the Cahn-Hilliard-Brinkman(CHB) system. In theory, it is strictly proved that the designed schemes are unconditionally energy-stable. With the delicate treatment of adaptive strategies, we propose several adaptive time-stepping algorithms to enhance the robustness of the schemes. More importantly, a novel hybrid-order adaptive time steps algorithm performs outstanding for the coupled system. The hybrid-order algorithm inherits the advantages of some traditional high-order BDF adaptive strategies. A comprehensive comparison with some adaptive time-stepping algorithms is given, and the advantages of the new adaptive time-stepping algorithms are emphasized. Finally, the effectiveness and accuracy of the new methods are validated through a series of numerical experiments. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Computers & Mathematics with Applications is the property of Pergamon Press - An Imprint of Elsevier Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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      – Type: doi
        Value: 10.1016/j.camwa.2025.12.016
    Languages:
      – Code: eng
        Text: English
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      Pagination:
        PageCount: 16
        StartPage: 182
    Subjects:
      – SubjectFull: Relaxation methods (Mathematics)
        Type: general
      – SubjectFull: Numerical analysis
        Type: general
      – SubjectFull: Cahn-Hilliard-Cook equation
        Type: general
      – SubjectFull: Simulation methods & models
        Type: general
      – SubjectFull: Iterative methods (Mathematics)
        Type: general
      – SubjectFull: Stability of linear systems
        Type: general
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      – TitleFull: New highly efficient and accurate numerical scheme for the Cahn-Hilliard-Brinkman system.
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            NameFull: Chen, Dawei
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            NameFull: Ren, Qinzhen
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            NameFull: Li, Minghui
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            – D: 15
              M: 02
              Text: Feb2026
              Type: published
              Y: 2026
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