A Study of the Partition of Unity-based T3-CNS and T3-DNS Finite Elements in Surface Fitting - Istiono, Heri; Tjong, Wong Foek (Institute of Research and Community Outreach - Petra Christian University, 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.