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

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Bibliographic Details
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]
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Database:	Engineering Source

Description
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]
ISSN:	14109530
DOI:	10.9744/ced.28.1.11-22