The lowest order characteristic mixed finite element scheme for convection-dominated diffusion problem

被引：6

作者：

Shi, Dongyang ^{[1
]}

Liao, Xin ^{[1
]}

Wang, Lele ^{[1
]}

机构：

[1] Zhengzhou Univ, Sch Math & Stat, Zhengzhou 450001, Peoples R China

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2014年 / 68卷 / 07期

基金：

中国国家自然科学基金;

关键词：

Characteristics MFEM; Convection-dominated diffusion problem; Error estimates; VARIABLE-COEFFICIENT; INTEGRAL-EQUATION;

D O I：

10.1016/j.camwa.2014.07.027

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A new characteristic mixed finite element method (MFEM) is proposed by combining the method of characteristics with the new mixed variational formulation for the convection-dominated diffusion problem. The error estimates for both the original variable u and auxiliary variable (p) over right arrow are derived via the properties of the integral identity and mean value techniques. At the same time, some numerical experiments are provided to confirm validity of the theoretical analysis and excellent performance of the proposed method. (C) 2014 Elsevier Ltd. All rights reserved.

引用

页码：759 / 769

页数：11

共 34 条

[1] A CHARACTERISTICS-MIXED FINITE-ELEMENT METHOD FOR ADVECTION-DOMINATED TRANSPORT PROBLEMS
ARBOGAST, T
WHEELER, MF
[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 1995, 32 (02) : 404 - 424
[2] AN EULERIAN-LAGRANGIAN LOCALIZED ADJOINT METHOD FOR THE ADVECTION-DIFFUSION EQUATION
CELIA, MA
RUSSELL, TF
HERRERA, I
EWING, RE
[J]. ADVANCES IN WATER RESOURCES, 1990, 13 (04) : 187 - 206
[3] A characteristics-mixed covolume method for a convection-dominated transport problem
Che, Haitao
Jiang, Ziwen
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2009, 231 (02) : 760 - 770
[4] A two-grid characteristic finite volume element method for semilinear advection-dominated diffusion equations
Chen, Chuanjun
Liu, Wei
Bi, Chunjia
[J]. NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2013, 29 (05) : 1543 - 1562
[5] [陈凤欣 CHEN Fengxin], 2009, [系统科学与数学, Journal of Systems Science and Mathematical Sciences], V29, P585
[6] [陈竑焘 Chen Hongtao], 2011, [数学的实践与认识, Mathematics in Practice and Theory], V41, P188
[7] [陈绍春 Chen Shaochun], 2010, [计算数学, Mathematica Numerica Sinica], V32, P213
[8] Characteristic-nonconforming finite-element methods for advection-dominated diffusion problems
Chen, ZX
[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2004, 48 (7-8) : 1087 - 1100
[9] CIARLET P. G., 2002, Classics in Appl. Math., V40
[10] Reliable and efficient error control for an adaptive Galerkin-characteristic method for convection-dominated diffusion problems
Cui, Ming
Chen, Zhangxin
Ewing, Richard E.
Qin, Guan
Chen, Hongsen
[J]. ADVANCES IN COMPUTATIONAL MATHEMATICS, 2012, 37 (03) : 319 - 353

← 1 2 3 4 →