Node-based S-FEM The smoothing domain is supported by elements containing the node in the triangular (T3) elements or tetrahedron (T4) elements. The sub-smoothing domain in each element is a quadrangle consisting of the node and two midpoint of the connected edge and the center of the supporting element in 2D. The first paper about Node-based SFEM was published in 2005. As shown in Fig. 2, not only does it lead to many new extensions to specific problems [34–37], but it also provides strong support for the Hybrid type of SFEM because of the feature of upper bound solution [38–40].