An Energy-Stable Minimal Deformation Rate Scheme for Mean Curvature Flow and Surface Diffusion.
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| Title: | An Energy-Stable Minimal Deformation Rate Scheme for Mean Curvature Flow and Surface Diffusion. |
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| Authors: | Gao, Guangwei1 (AUTHOR) guang-wei.gao@polyu.edu.hk, Garcke, Harald2 (AUTHOR) harald.garcke@mathematik.uni-regensburg.de, Li, Buyang1 (AUTHOR) buyang.li@polyu.edu.hk, Tang, Rong1 (AUTHOR) claire.tang@polyu.edu.hk |
| Source: | SIAM Journal on Scientific Computing. 2026, Vol. 48 Issue 1, pA103-A131. 29p. |
| Subjects: | Surface diffusion, Finite element method, Iterative methods (Mathematics), Numerical analysis, Conservation of energy, Strain rate |
| Abstract: | We propose a new parametric finite element method, referred to as the BGN-MDR method, for simulating both mean curvature flow and surface diffusion for closed hypersurfaces, as well as open hypersurfaces with moving contact lines in three dimensions. The method is also applicable to closed and open curves with moving contact points in two dimensions. The proposed scheme inherits the energy stability from the BGN scheme proposed by Barrett, Garcke, and Nürnberg in 2008 and offers improved mesh quality similar to the minimal deformation rate (MDR) method proposed by Hu and Li in 2022, especially for small time step sizes where the BGN scheme may become unstable and result in deteriorated meshes. [ABSTRACT FROM AUTHOR] |
| Copyright of SIAM Journal on Scientific Computing is the property of Society for Industrial & Applied Mathematics 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 |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 192099083 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: An Energy-Stable Minimal Deformation Rate Scheme for Mean Curvature Flow and Surface Diffusion. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Gao%2C+Guangwei%22">Gao, Guangwei</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> guang-wei.gao@polyu.edu.hk</i><br /><searchLink fieldCode="AR" term="%22Garcke%2C+Harald%22">Garcke, Harald</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> harald.garcke@mathematik.uni-regensburg.de</i><br /><searchLink fieldCode="AR" term="%22Li%2C+Buyang%22">Li, Buyang</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> buyang.li@polyu.edu.hk</i><br /><searchLink fieldCode="AR" term="%22Tang%2C+Rong%22">Tang, Rong</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> claire.tang@polyu.edu.hk</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22SIAM+Journal+on+Scientific+Computing%22">SIAM Journal on Scientific Computing</searchLink>. 2026, Vol. 48 Issue 1, pA103-A131. 29p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Surface+diffusion%22">Surface diffusion</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+element+method%22">Finite element method</searchLink><br /><searchLink fieldCode="DE" term="%22Iterative+methods+%28Mathematics%29%22">Iterative methods (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Conservation+of+energy%22">Conservation of energy</searchLink><br /><searchLink fieldCode="DE" term="%22Strain+rate%22">Strain rate</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: We propose a new parametric finite element method, referred to as the BGN-MDR method, for simulating both mean curvature flow and surface diffusion for closed hypersurfaces, as well as open hypersurfaces with moving contact lines in three dimensions. The method is also applicable to closed and open curves with moving contact points in two dimensions. The proposed scheme inherits the energy stability from the BGN scheme proposed by Barrett, Garcke, and Nürnberg in 2008 and offers improved mesh quality similar to the minimal deformation rate (MDR) method proposed by Hu and Li in 2022, especially for small time step sizes where the BGN scheme may become unstable and result in deteriorated meshes. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of SIAM Journal on Scientific Computing is the property of Society for Industrial & Applied Mathematics 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: BibEntity: Identifiers: – Type: doi Value: 10.1137/25M1753838 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 29 StartPage: A103 Subjects: – SubjectFull: Surface diffusion Type: general – SubjectFull: Finite element method Type: general – SubjectFull: Iterative methods (Mathematics) Type: general – SubjectFull: Numerical analysis Type: general – SubjectFull: Conservation of energy Type: general – SubjectFull: Strain rate Type: general Titles: – TitleFull: An Energy-Stable Minimal Deformation Rate Scheme for Mean Curvature Flow and Surface Diffusion. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Gao, Guangwei – PersonEntity: Name: NameFull: Garcke, Harald – PersonEntity: Name: NameFull: Li, Buyang – PersonEntity: Name: NameFull: Tang, Rong IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Text: 2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 10648275 Numbering: – Type: volume Value: 48 – Type: issue Value: 1 Titles: – TitleFull: SIAM Journal on Scientific Computing Type: main |
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