Asymptotic streamline diffusion finite element method for singularly perturbed convection–diffusion differential difference equations

2021 ◽  
Author(s):  
Senthilkumar L.S. ◽  
Subburayan Veerasamy ◽  
Ravi P. Agarwal
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Difference Equations ◽  
Singularly Perturbed ◽  
Convection Diffusion ◽  
Streamline Diffusion ◽  
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.

scholarly journals THE HP-VERSION OF THE STREAMLINE DIFFUSION FINITE ELEMENT METHOD IN TWO SPACE DIMENSIONS

2001 ◽  
Vol 11 (02) ◽  
pp. 301-337 ◽  
Author(s):  
K. GERDES ◽  
J. M. MELENK ◽  
C. SCHWAB ◽  
D. SCHÖTZAU
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Rates Of Convergence ◽  
Diffusion Problem ◽  
Convection Diffusion ◽  
Consistency Results ◽  
Two Space Dimensions ◽  
Streamline Diffusion ◽  
Exponential Rates ◽  
Element Method

The Streamline Diffusion Finite Element Method (SDFEM) for a two-dimensional convection–diffusion problem is analyzed in the context of the hp-version of the Finite Element Method (FEM). It is proved that the appropriate choice of the SDFEM parameters leads to stable methods on the class of "boundary layer meshes", which may contain anisotropic needle elements of arbitrarily high aspect ratio. Consistency results show that the use of such meshes can resolve layer components present in the solutions at robust exponential rates of convergence. We confirm these theoretical results in a series of numerical examples.

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