A novel node-based smoothed polygonal finite element method with reconstructed strain fields for solving heat conduction problems

• Published in: International journal of heat and mass transfer Vol. 248; p. 127195
• Main Authors: Zhao, Shijie, Niu, Ruiping, Lu, Xinglong, Wu, Chengtao, Li, Siqing
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 15.09.2025
• Subjects: Heat conduction problem; High-order smoothed finite element method; Polygonal finite element method; Thermal strain field reconstruction; Wachspress shape function; Wachspress shape function; Thermal strain field reconstruction; High-order smoothed finite element method; Polygonal finite element method; Heat conduction problem
• ISSN: 0017-9310
• DOI: 10.1016/j.ijheatmasstransfer.2025.127195

•NS-PFEM-1 has the best accuracy in both temperature and energy solutions. Although NS-PFEM-2 performs better than NS-PFEM, PFEM, FEM-T3 and ES-FEM-T3 it is less precise and effective than NSPFEM-1.•NS-PFEM-1 have higher computational efficiency than NS-PFEM, PFEM, FEM-T3 and ES-FEM-T3 with the same mesh. NS-PFEM-1 are more effective when taking into account accuracy and CPU times.•Both NSPFEM-1 and NSPFEM-2 exhibit strong super-convergence in temperature and energy norm.•NS-PFEM-1 and NS-PFEM-2 can produce much more accurate thermal strain solutions compared to the standard NS-PFEM and PFEM.•Compared to standard finite elements, such as triangular and quadrilateral, polygonal elements offer superior computational accuracy and faster convergence rates.•NS-PFEM-1 and NS-PFEM-2 can produce much more accurate temperature and heat flux solutions compared to the standard, thereby validating the practical applicability of the proposed methodologies. This paper presents a novel node-based smoothed polygonal finite element method (NS-PFEM) with reconstructed strain fields for solving heat conduction problems. In order to approximate the thermal strain field in Wachspress coordinates, the high-order smoothed thermal strain field is constructed using pick-out theory. Two high-order S-FEM models have been developed: NS-PFEM-1 for linear thermal strain and NS-PFEM-2 for second-order thermal strain. By employing the gradient smoothing technique, the shape function values on the boundaries of node-based smoothing domains are required rather than the derivatives of the shape function, which reduces the continuity requirements for shape functions. It also eliminates the isoparametric mapping in polygonal finite element methods, which can significantly enhance computational efficiency. The performance of the high-order NS-PFEMs is rigorously examined against the standard NS-PFEM, PFEM, FEM-T3, ES-FEM-T3 and the finite element software COMSOL. Numerical examples demonstrate that our high-order NS-PFEMs produce super convergent and nearly exact solutions in both temperature and energy at low computational costs.