Convergence analysis of streamline diffusion finite element method on two types of meshes for convection–diffusion problems

Kexin Han, Jin Zhang and Jinghui Li

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 249, issue C, 191-207

Abstract: This paper focuses on the streamline-diffusion nonconforming finite element method when it is applied to convection–diffusion problems on both quasi-uniform meshes and Shishkin meshes. For quasi-uniform meshes, additional terms are introduced to improve the condition number of the resulting linear systems. Furthermore, we apply this method to Shishkin meshes for the first time and prove uniform convergence of almost optimal order in an energy norm. Numerical experiments clearly demonstrate that the method in this paper indeed improves the condition number of the numerical algorithm on quasi-uniform meshes and strongly verifies our analysis of the convergence order.

Keywords: Nonconforming finite element; Streamline diffusion finite element method (SDFEM); Shishkin triangular mesh; Convergence (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:249:y:2026:i:c:p:191-207

DOI: 10.1016/j.matcom.2026.04.039

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