scholarly journals The Sdfem for a Convection-diffusion Problem with Two Small Parameters

2003 ◽  
Vol 3 (3) ◽  
pp. 443-458 ◽  
Author(s):  
Hans-Görg Roos ◽  
Zorica Uzelac
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Experiments ◽  
Diffusion Problem ◽  
Shishkin Mesh ◽  
Singularly Perturbed ◽  
Convection Diffusion ◽  
Small Parameters ◽  
Perturbation Parameters ◽  
Theoretical Results

AbstractA singularly perturbed convection-diffusion problem with two small parameters is considered. The problem is solved using the streamline-diffusion finite element method on a Shishkin mesh. We prove that the method is convergent independently of the perturbation parameters. Numerical experiments support these theoretical results.

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.

Error Analysis for a Non-Monotone FEM for a Singularly Perturbed Problem with Two Small Parameters

2015 ◽  
Vol 7 (2) ◽  
pp. 196-206
Author(s):  
Yanping Chen ◽  
Haitao Leng ◽  
Li-Bin Liu
Keyword(s):  
Error Bound ◽  
A Priori ◽  
Diffusion Problem ◽  
Singularly Perturbed ◽  
Singularly Perturbed Problem ◽  
Optimal Error ◽  
Convection Diffusion ◽  
Small Parameters ◽  
Perturbation Parameters ◽  
Optimal Error Bound

AbstractIn this paper, we consider a singularly perturbed convection-diffusion problem. The problem involves two small parameters that gives rise to two boundary layers at two endpoints of the domain. For this problem, a non-monotone finite element methods is used. A priori error bound in the maximum norm is obtained. Based on the a priori error bound, we show that there exists Bakhvalov-type mesh that gives optimal error bound of (N−2) which is robust with respect to the two perturbation parameters. Numerical results are given that confirm the theoretical result.

scholarly journals Supercloseness Result of Higher Order FEM/LDG Coupled Method for Solving Singularly Perturbed Problem on S-Type Mesh

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Shenglan Xie ◽  
Huonian Tu ◽  
Peng Zhu
Keyword(s):  
Numerical Experiments ◽  
Diffusion Problem ◽  
Higher Order ◽  
Singularly Perturbed ◽  
Singularly Perturbed Problem ◽  
Piecewise Polynomial ◽  
Coupled Method ◽  
Convection Diffusion ◽  
Polynomial Approximations ◽  
Theoretical Results

we present a first supercloseness analysis for higher order FEM/LDG coupled method for solving singularly perturbed convection-diffusion problem. Based on piecewise polynomial approximations of degreek  (k≥1), a supercloseness property ofk+1/2in DG norm is established on S-type mesh. Numerical experiments complement the theoretical results.

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