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A Study of the Partition of Unity-based T3-CNS and T3-DNS Finite Elements in Surface Fitting.

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Title: A Study of the Partition of Unity-based T3-CNS and T3-DNS Finite Elements in Surface Fitting.
Authors: Istiono, H.1,2, Wong, F. T.1 wftjong@petra.ac.id
Source: Civil Engineering Dimension. Mar2026, Vol. 28 Issue 1, p11-22. 12p.
Subjects: Partition of unity method, Finite element method, Galerkin methods, Numerical analysis, Numerical solutions to partial differential equations
Abstract: Various alternative, enhanced finite element methods (FEMs) have been proposed to improve the accuracy and convergence of traditional FEM. One promising approach is the hybrid FEM-meshfree method using the partition of unity concept. This study examines the performance of two variants of the hybrid-meshfree method: the three-node triangular element with continuous nodal stress (T3-CNS) and the three-node triangular element with discontinuous nodal stress (T3-DNS). These methods are evaluated in the context of surface fitting through numerical tests. Their accuracy and convergence are compared with the standard triangular element and Kriging-based FEM. The results show that both T3-CNS and T3-DNS methods maintain consistency and yield accurate surface approximations with good convergence. However, their performance declines in problems involving gradient singularities. This study enhances the understanding of T3-CNS and T3-DNS interpolations, providing insights into their application in a Galerkin method for solving engineering model problems. [ABSTRACT FROM AUTHOR]
Copyright of Civil Engineering Dimension is the property of Institute of Research & Community Outreach - Petra Christian University 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.)
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  Data: A Study of the Partition of Unity-based T3-CNS and T3-DNS Finite Elements in Surface Fitting.
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  Data: <searchLink fieldCode="JN" term="%22Civil+Engineering+Dimension%22">Civil Engineering Dimension</searchLink>. Mar2026, Vol. 28 Issue 1, p11-22. 12p.
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  Data: <searchLink fieldCode="DE" term="%22Partition+of+unity+method%22">Partition of unity method</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+element+method%22">Finite element method</searchLink><br /><searchLink fieldCode="DE" term="%22Galerkin+methods%22">Galerkin methods</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+solutions+to+partial+differential+equations%22">Numerical solutions to partial differential equations</searchLink>
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  Label: Abstract
  Group: Ab
  Data: Various alternative, enhanced finite element methods (FEMs) have been proposed to improve the accuracy and convergence of traditional FEM. One promising approach is the hybrid FEM-meshfree method using the partition of unity concept. This study examines the performance of two variants of the hybrid-meshfree method: the three-node triangular element with continuous nodal stress (T3-CNS) and the three-node triangular element with discontinuous nodal stress (T3-DNS). These methods are evaluated in the context of surface fitting through numerical tests. Their accuracy and convergence are compared with the standard triangular element and Kriging-based FEM. The results show that both T3-CNS and T3-DNS methods maintain consistency and yield accurate surface approximations with good convergence. However, their performance declines in problems involving gradient singularities. This study enhances the understanding of T3-CNS and T3-DNS interpolations, providing insights into their application in a Galerkin method for solving engineering model problems. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Group: Ab
  Data: <i>Copyright of Civil Engineering Dimension is the property of Institute of Research & Community Outreach - Petra Christian University 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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        Value: 10.9744/ced.28.1.11-22
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        Text: English
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      – SubjectFull: Partition of unity method
        Type: general
      – SubjectFull: Finite element method
        Type: general
      – SubjectFull: Galerkin methods
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      – SubjectFull: Numerical analysis
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      – SubjectFull: Numerical solutions to partial differential equations
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              Text: Mar2026
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