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.

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.

scholarly journals A Numerical Method for a Singularly Perturbed Three-Point Boundary Value Problem

2010 ◽  
Vol 2010 ◽  
pp. 1-17 ◽  
Author(s):  
Musa Çakır ◽  
Gabil M. Amiraliyev
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Numerical Method ◽  
Numerical Experiments ◽  
Diffusion Problem ◽  
Singularly Perturbed ◽  
Point Boundary ◽  
Convection Diffusion ◽  
First Order ◽  
Type Boundary

The purpose of this paper is to present a uniform finite difference method for numerical solution of nonlinear singularly perturbed convection-diffusion problem with nonlocal and third type boundary conditions. The numerical method is constructed on piecewise uniform Shishkin type mesh. The method is shown to be convergent, uniformly in the diffusion parameterε, of first order in the discrete maximum norm. Some numerical experiments illustrate in practice the result of convergence proved theoretically.

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.

Finite Difference Schemes for Convection-diffusion Problems with a Concentrated Source and a Discontinuous Convection Field

2001 ◽  
Vol 2 (1) ◽  
pp. 41-49 ◽  
Author(s):  
Torsten Linß
Keyword(s):  
Numerical Experiments ◽  
Perturbation Parameter ◽  
Diffusion Problem ◽  
Difference Schemes ◽  
Finite Difference Schemes ◽  
Convection Diffusion ◽  
Concentrated Source ◽  
General Meshes ◽  
Theoretical Results ◽  
Diffusion Problems

AbstractA singularly perturbed convection-diffusion problem with a concentrated source is considered. The problem is solved numerically using two upwind difference schemes on general meshes. We prove convergence, uniformly with respect to the perturbation parameter, in the discrete maximum norm on Shishkin and Bakhvalov meshes. Numerical experiments complement our 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.

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