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Yosef, T.Y., Fang, C., Faller, R.K., Kim, S., Bielenberg, R.W., Stolle, C.S., et al. (2024) Adaptive Coupling of FEM and SPH Method for Simulating Dynamic Post-Soil Interaction under Impact Loading. Advances in Engineering Software, 195, Article ID: 103707.
https://doi.org/10.1016/j.advengsoft.2024.103707

has been cited by the following article:

• TITLE: A New Efficient h-Type Adaptive Analysis Procedure for Finite Element Method

  AUTHORS: Qian Tang, Jiande Wang, Yu Ren

  KEYWORDS: Adaptive Analysis, Error Indicator, FEM, H-Type Refinement, Delaunay Triangulation

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.13 No.9, September 26, 2025

  ABSTRACT: This paper focuses on constructing the adaptive analysis model based on the Finite Element Method (FEM) with an unstructured mesh, which includes taking full advantage of the two-dimensional triangle’s ability to discretize any complex model. The error indicator and h-type refinement scheme for FEM has been presented by providing a simple error indicator based on the difference value of nodal fundamental physical variables. It provides an effective measure of the error in the numerical solution, which can lead to an adaptive refinement scheme, determining the optimal location of new inserted nodes that are mainly distributed in the local high stress gradient domain. A numerical experiment is presented to demonstrate that the proposed error indicator reasonably tracks the distribution of the true error, and the effectiveness of the proposed adaptive analysis procedure, which achieves significantly higher convergence rates compared to the uniform mesh.