Numerical approximation of two-dimensional convection-diffusion equations with multiple boundary layers

被引：0
|
作者：
Jung, Chang-Yeol [1 ]
Temam, Roger
机构：
[1] Indiana Univ, Inst Sci Comp & Appl Math, Bloomington, IN 47405 USA
[2] Univ Paris 11, Anal Numer Lab, F-91405 Orsay, France
来源：
INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING | 2005年 / 2卷 / 04期
关键词：
boundary layers; finite elements; singularly perturbed problem; convection-diffusion;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this article, we demonstrate how one can improve the numerical solutions of singularly perturbed problems involving multiple boundary layers by using a combination of analytic and numerical tools. Incorporating the structures of boundary layers into finite element spaces can improve the accuracy of approximate solutions and result in significant simplifications. We discuss here convection-diffusion equations in the case where both ordinary and parabolic boundary layers are present.
引用
收藏
页码：367 / 408
页数：42
相关论文
共 50 条
  • [1] Numerical approximation of two-dimensional convection-diffusion equations with boundary layers
    Jung, CY
    [J]. NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2005, 21 (03) : 623 - 648
  • [2] A boundary element numerical scheme for the two-dimensional convection-diffusion equation
    Romero, Luis M.
    Benitez, Francisco G.
    [J]. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2008, 76 (13) : 2063 - 2090
  • [3] A numerical method for two-dimensional transient nonlinear convection-diffusion equations
    Meng, Xiangyuan
    Huang, Mei
    Wang, Boxue
    Ouyang, Xiaoping
    Huang, Yanping
    Chen, Denggao
    Cheng, Yanting
    Li, Yaodi
    [J]. ANNALS OF NUCLEAR ENERGY, 2024, 205
  • [4] Numerical approximation of convection-diffusion equations in a channel using boundary layer elements
    Jung, CY
    [J]. APPLIED NUMERICAL MATHEMATICS, 2006, 56 (06) : 756 - 777
  • [5] On parabolic boundary layers for convection-diffusion equations in a channel: Analysis and numerical applications
    Jung, Chang-Yeol
    Temam, Roger
    [J]. JOURNAL OF SCIENTIFIC COMPUTING, 2006, 28 (2-3) : 361 - 410
  • [6] A half boundary method for two dimensional unsteady convection-diffusion equations
    Zhao, Yuanyuan
    Huang, Mei
    Ouyang, Xiaoping
    Luo, Jun
    Shen, Yongqing
    Bao, Fang
    [J]. ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 2022, 135 : 322 - 336
  • [7] On the Numerical Approximation of Three-Dimensional Time Fractional Convection-Diffusion Equations
    Kamal, Raheel
    Rahmat, Gul
    Shah, Kamal
    [J]. MATHEMATICAL PROBLEMS IN ENGINEERING, 2021, 2021
  • [8] THE COMBINATION TECHNIQUE FOR A TWO-DIMENSIONAL CONVECTION-DIFFUSION PROBLEM WITH EXPONENTIAL LAYERS
    Franz, Sebastian
    Liu, Fang
    Roos, Hans-Goerg
    Stynes, Martin
    Zhou, Aihui
    [J]. APPLICATIONS OF MATHEMATICS, 2009, 54 (03) : 203 - 223
  • [9] Half boundary method for two-dimensional steady-state nonlinear convection-diffusion equations
    Meng, Xiangyuan
    Huang, Mei
    Wang, Boxue
    Li, Yaodi
    Cheng, Yanting
    Morita, Chihiro
    [J]. ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 2023, 150 : 187 - 198
  • [10] The combination technique for a two-dimensional convection-diffusion problem with exponential layers
    Sebastian Franz
    Fang Liu
    Hans-Görg Roos
    Martin Stynes
    Aihui Zhou
    [J]. Applications of Mathematics, 2009, 54 : 203 - 223
12345