Boundary enhancement of the smoothed finite element method

The smoothed finite element method (S-FEM) is an effective approach that improves the accuracy of conventional FEM solutions without increasing the total number of degrees of freedom. However, its accuracy is highly dependent on the definition of the smoothing domain. In particular, boundary smoothing domains are less effective due to the limited number of adjacent elements, and boundary elements tend to be stiffer than interior elements, leading to significant accuracy degradation near the boundaries. In this study, a modified approach is proposed to enhance the boundary approximation performance of S-FEM. Numerical examples demonstrate that the accuracy of edge-based S-FEM solutions can be significantly improved through boundary modification. The proposed method is further extended to three-dimensional tetrahedral elements, but in 3-D cases, the overall improvement in accuracy remains limited. This is attributed to the fact that, unlike in 2-D cases, interior smoothing in face-based S-FEM does not contribute significantly to accuracy enhancement in three-dimensional problems.