A new combined finite element-upwind finite volume method for convection-dominated diffusion problems

被引：5

作者：

Wang, Cheng ^{[1
]}

He, Mingyan ^{[2
]}

Sun, Pengtao ^{[3
]}

机构：

[1] Tongji Univ, Dept Math, Shanghai 200092, Peoples R China

[2] Hangzhou Dianzi Univ, Sch Sci, Hangzhou 310018, Zhejiang, Peoples R China

[3] Univ Nevada, Dept Math Sci, Las Vegas, NV 89154 USA

来源：

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS | 2016年 / 32卷 / 03期

基金：

美国国家科学基金会;

关键词：

convection-dominated; high-order accuracy; numerical experiments; stability; weighted upwind finite volume method; COMPUTATIONAL FLUID-DYNAMICS; SCALAR CONSERVATION-LAWS; MODEL; CONVERGENCE; FORMULATION; EQUATION; SCHEMES; DOMAIN; GRIDS;

D O I：

10.1002/num.22027

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we develop a combined finite element-weighted upwind finite volume method for convection-dominated diffusion problems in two dimensions, which discretizes the diffusion term with the standard finite element scheme, and the convection and source terms with the weighted upwind finite volume scheme. The developed method leads to a totally new scheme for convection-dominated problems, which overcomes numerical oscillation, avoids numerical dispersion, and has high-order accuracy. Stability analyses of the scheme are given for the problems with constant coefficients. Numerical experiments are presented to illustrate the stability and optimal convergence of our proposed method. (c) 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 799-818, 2016

引用

页码：799 / 818

页数：20

共 50 条

[31] A finite element method with residual-free bubbles for convection-dominated diffusion equations
Liu, Dajin
Li, Wentao
[J]. PROCEEDINGS OF FIRST INTERNATIONAL CONFERENCE OF MODELLING AND SIMULATION, VOL II: MATHEMATICAL MODELLING, 2008, : 326 - 330
[32] A New Characteristic Nonconforming Mixed Finite Element Scheme for Convection-Dominated Diffusion Problem
Shi, Dongyang
Tang, Qili
Zhang, Yadong
[J]. JOURNAL OF APPLIED MATHEMATICS, 2013,
[33] On the convergence of a combined finite volume-finite element method for nonlinear convection-diffusion problems
[J]. Numer Methods Partial Differential Equations, 2 (163):
[34] Convergence of an upwind control-volume mixed finite element method for convection-diffusion problems
Rui, H.
[J]. COMPUTING, 2007, 81 (04) : 297 - 315
[35] An Upwind Finite Volume Element Method Based on Quadrilateral Meshes for Nonlinear Convection-Diffusion Problems
Gao, Fu-Zheng
Yuan, Yi-Rang
[J]. NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2009, 25 (05) : 1067 - 1085
[36] An upwind finite volume element method on a Shishkin mesh for singularly perturbed convection-diffusion problems
Wang, Yue
Li, Yonghai
Meng, Xiangyun
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2024, 438
[37] An enriched Galerkin-characteristics finite element method for convection-dominated and transport problems
Ouardghi, Abdelouahed
El-Amrani, Mofdi
Seaid, Mohammed
[J]. APPLIED NUMERICAL MATHEMATICS, 2021, 167 : 119 - 142
[38] On the stabilized finite element method for steady convection-dominated problems with anisotropic mesh adaptation
Hachem, E.
Jannoun, G.
Veysset, J.
Coupez, T.
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2014, 232 : 581 - 594
[39] On uniform convergence rates for Eulerian and Lagrangian finite element approximations of convection-dominated diffusion problems
M. Bause
P. Knabner
[J]. CALCOLO, 2004, 41 : 1 - 26
[40] On uniform convergence rates for Eulerian and Lagrangian finite element approximations of convection-dominated diffusion problems
Bause, M
Knabner, P
[J]. CALCOLO, 2004, 41 (01) : 1 - 26

← 1 2 3 4 5 →