Convergence and supercloseness of a finite element method for a two-parameter singularly perturbed problem on Shishkin triangular mesh

2022 ◽  
Vol 416 ◽  
pp. 126753
Author(s):  
Yanhui Lv ◽  
Jin Zhang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Triangular Mesh ◽  
Singularly Perturbed ◽  
Singularly Perturbed Problem ◽  
Shishkin Triangular Mesh ◽  
Two Parameter ◽  
Element Method

A finite element method for two–parameter singularly perturbed problems in 2D

PAMM ◽  
2006 ◽  
Vol 6 (1) ◽  
pp. 771-772 ◽  
Author(s):  
Ljiljana Teofanov ◽  
Hans-Görg Roos ◽  
Helena Zarin
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Singularly Perturbed ◽  
Singularly Perturbed Problems ◽  
Two Parameter ◽  
Element Method

Analysis of a Streamline-Diffusion Finite Element Method on Bakhvalov-Shishkin Mesh for Singularly Perturbed Problem

2017 ◽  
Vol 10 (1) ◽  
pp. 44-64 ◽  
Author(s):  
Yunhui Yin ◽  
Peng Zhu ◽  
Bin Wang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Perturbation Parameter ◽  
Diffusion Problem ◽  
Shishkin Mesh ◽  
Singularly Perturbed ◽  
Singularly Perturbed Problem ◽  
Convection Diffusion ◽  
Streamline Diffusion ◽  
Element Method

AbstractIn this paper, a bilinear Streamline-Diffusion finite element method on Bakhvalov-Shishkin mesh for singularly perturbed convection – diffusion problem is analyzed. The method is shown to be convergent uniformly in the perturbation parameter ∈ provided only that ∈ ≤ N–1. An convergent rate in a discrete streamline-diffusion norm is established under certain regularity assumptions. Finally, through numerical experiments, we verified the theoretical results.

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