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Level-set based interface propagation: a stabilized least-squares polygonal finite element computation.

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Title: Level-set based interface propagation: a stabilized least-squares polygonal finite element computation.
Authors: Nguyen, Son H.1,2 (AUTHOR) son.nguyenhoang@vlu.edu.vn, Nguyen-Tran, Ba-Dinh1,2,3 (AUTHOR), Phan, Duc-Huynh3 (AUTHOR), Ngo, Long Cu4 (AUTHOR), Ha, Sang Truong5 (AUTHOR)
Source: Computers & Mathematics with Applications. Jun2026, Vol. 211, p184-199. 16p.
Subjects: Level set methods, Finite element method, Least squares, Numerical analysis, Laplacian operator
Abstract: In this paper, a stabilized least-squares polygonal finite element method, named as LeSq-Poly, is introduced to address the evolution of a level-set function and its re-initialization process. Unlike conventional triangular and quadrilateral elements, our approach utilizes polygonal meshes for spatial discretization, offering increased flexibility in mesh generation and yielding more precise solutions. To stabilize numerical solutions without non-physical oscillations (steep gradients), both level-set evolution and its re-initialization are solved by using a stabilized least-squares minimization. In addition, a simple and efficient Laplacian smoothing technique is imposed to alleviate the mass-loss phenomenon due to adding diffusion terms in both level-set evolution and its re-initialization. Three benchmark problems are considered in numerical experiments: ellipse re-initialization, Zalesak's disk rotation, and vortex flow of a circular fluid body. The numerical results demonstrate that the LeSq-Poly approach effectively provides stable and reliable solutions. [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
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  Data: Level-set based interface propagation: a stabilized least-squares polygonal finite element computation.
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  Data: <searchLink fieldCode="JN" term="%22Computers+%26+Mathematics+with+Applications%22">Computers & Mathematics with Applications</searchLink>. Jun2026, Vol. 211, p184-199. 16p.
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  Data: <searchLink fieldCode="DE" term="%22Level+set+methods%22">Level set methods</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+element+method%22">Finite element method</searchLink><br /><searchLink fieldCode="DE" term="%22Least+squares%22">Least squares</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Laplacian+operator%22">Laplacian operator</searchLink>
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  Label: Abstract
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  Data: In this paper, a stabilized least-squares polygonal finite element method, named as LeSq-Poly, is introduced to address the evolution of a level-set function and its re-initialization process. Unlike conventional triangular and quadrilateral elements, our approach utilizes polygonal meshes for spatial discretization, offering increased flexibility in mesh generation and yielding more precise solutions. To stabilize numerical solutions without non-physical oscillations (steep gradients), both level-set evolution and its re-initialization are solved by using a stabilized least-squares minimization. In addition, a simple and efficient Laplacian smoothing technique is imposed to alleviate the mass-loss phenomenon due to adding diffusion terms in both level-set evolution and its re-initialization. Three benchmark problems are considered in numerical experiments: ellipse re-initialization, Zalesak's disk rotation, and vortex flow of a circular fluid body. The numerical results demonstrate that the LeSq-Poly approach effectively provides stable and reliable solutions. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
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  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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    Identifiers:
      – Type: doi
        Value: 10.1016/j.camwa.2026.03.025
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 16
        StartPage: 184
    Subjects:
      – SubjectFull: Level set methods
        Type: general
      – SubjectFull: Finite element method
        Type: general
      – SubjectFull: Least squares
        Type: general
      – SubjectFull: Numerical analysis
        Type: general
      – SubjectFull: Laplacian operator
        Type: general
    Titles:
      – TitleFull: Level-set based interface propagation: a stabilized least-squares polygonal finite element computation.
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            NameFull: Nguyen, Son H.
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            NameFull: Nguyen-Tran, Ba-Dinh
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            NameFull: Phan, Duc-Huynh
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            NameFull: Ngo, Long Cu
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            NameFull: Ha, Sang Truong
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            – D: 01
              M: 06
              Text: Jun2026
              Type: published
              Y: 2026
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              Value: 211
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