ERROR ESTIMATES OF THE FINITE ELEMENT METHOD WITH WEIGHTED BASIS FUNCTIONS FOR A SINGULARLY PERTURBED CONVECTION-DIFFUSION EQUATION

被引：0

作者：

Li, Xianggui ^{[1
]}

Yu, Xijun ^{[2
]}

Chen, Guangnan ^{[2
]}

机构：

[1] Beijing Informat Sci & Technol Univ, Sch Appl Sci, Beijing 100101, Peoples R China

[2] Inst Appl Phys & Computat Math, Beijing 100088, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL MATHEMATICS | 2011年 / 29卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Convergence; Singular perturbation; Convection-diffusion equation; Finite element method; ADAPTED MESHES;

D O I：

10.4208/jcm.1009-m3113

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we establish a convergence theory for a finite element method with weighted basis functions for solving singularly perturbed convection-diffusion equations. The stability of this finite element method is proved and an upper bound O(h vertical bar ln epsilon vertical bar(3/2)) for errors in the approximate solutions in the energy norm is obtained on the triangular Bakhvalov-type mesh. Numerical results are presented to verify the stability and the convergent rate of this finite element method.

引用

页码：227 / 242

页数：16

共 50 条

[41] Conditioning of a difference scheme of the solution decomposition method for a singularly perturbed convection-diffusion equation
Shishkin, G. I.
TRUDY INSTITUTA MATEMATIKI I MEKHANIKI URO RAN, 2012, 18 (02): : 291 - 304
[42] LOCAL ERROR-ESTIMATES FOR A FINITE-ELEMENT METHOD FOR HYPERBOLIC AND CONVECTION-DIFFUSION EQUATIONS
FALK, RS
RICHTER, GR
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1992, 29 (03) : 730 - 754
[43] Fitted scheme of the finite element method for a convection-diffusion equation
Karepova, ED
Shaidurov, VV
RUSSIAN JOURNAL OF NUMERICAL ANALYSIS AND MATHEMATICAL MODELLING, 2000, 15 (02) : 167 - 182
[44] A Streamline Diffusion Method for a Singularly Perturbed Conservative Convection-diffusion Problem
Cen, Zhongdi
Xi, Lifeng
CEA'09: PROCEEDINGS OF THE 3RD WSEAS INTERNATIONAL CONFERENCE ON COMPUTER ENGINEERING AND APPLICATIONS, 2009, : 211 - +
[45] Error estimates for a finite element-finite volume discretization of convection-diffusion equations
Deuring, Paul
Mildner, Marcus
APPLIED NUMERICAL MATHEMATICS, 2011, 61 (06) : 785 - 801
[46] A Finite Difference Scheme on a Priori Adapted Meshes for a Singularly Perturbed Parabolic Convection-Diffusion Equation
Shishkin, Grigory I.
NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS, 2008, 1 (02) : 214 - 234
[47] A Finite Difference Scheme on a Priori Adapted Meshes for a Singularly Perturbed Parabolic Convection-Diffusion Equation
Grigory I.Shishkin
NumericalMathematics:Theory,MethodsandApplications, 2008, MethodsandApplications.2008 (02) : 214 - 234
[48] A new stable method for singularly perturbed convection-diffusion equations
Ramakkagari, Viswanath
Flaherty, Joseph E.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2008, 197 (17-18) : 1507 - 1524
[49] GROUND STATES OF SINGULARLY PERTURBED CONVECTION-DIFFUSION EQUATION WITH OSCILLATING COEFFICIENTS
Piatnitski, A.
Rybalko, A.
Rybalko, V.
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2014, 20 (04) : 1059 - 1077
[50] Numerical method for a singularly perturbed convection-diffusion problem with delay
Amiraliyev, Gabil M.
Cimen, Erkan
APPLIED MATHEMATICS AND COMPUTATION, 2010, 216 (08) : 2351 - 2359

← 1 2 3 4 5 →