A Study of the Partition of Unity-based T3-CNS and T3-DNS Finite Elements in Surface Fitting - Istiono, Heri; Tjong, Wong Foek (Civil Engineering Dimension, 2026)
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.