数学物理学报(英文版)

• 论文 • 上一篇    下一篇

NUMERICAL SIMULATION FOR CONVECTION-DIFFUSION PROBLEM WITH PERIODIC MICRO-STRUCTURE

吴志华 ; 严宁宁   

  1. 中国科学院数学与系统科学研究院, 北京 100080
  • 收稿日期:2004-04-12 修回日期:2005-06-13 出版日期:2008-04-20 发布日期:2008-04-20
  • 通讯作者: 严宁宁

NUMERICAL SIMULATION FOR CONVECTION-DIFFUSION PROBLEM WITH PERIODIC MICRO-STRUCTURE

Wu Zhihua; Yan Ningning   

  1. Institute of System Sciences, Academy of Mathematics and System Sciences,
    Chinese Academy of Sciences, Beijing 100080, China
  • Received:2004-04-12 Revised:2005-06-13 Online:2008-04-20 Published:2008-04-20
  • Contact: Yan Ningning

摘要:

In this article, the convection dominated convection-diffusion problems with the periodic micro-structure are discussed. A two-scale finite element scheme based on the homogenization technique for this kind of problems is provided. The error estimates between the exact solution and the approximation solution of the homogenized equation or the two-scale finite element scheme are analyzed. It is shown that the scheme provided in this article is convergent for any fixed diffusion coefficient δ, and it may be convergent independent of δ under some conditions. The numerical results
demonstrating the theoretical results are presented in this article.

关键词: Convection-diffusion problem, homogenization, micro-structure, asymptotic expansion

Abstract:

In this article, the convection dominated convection-diffusion problems with the periodic micro-structure are discussed. A two-scale finite element scheme based on the homogenization technique for this kind of problems is provided. The error estimates between the exact solution and the approximation solution of the homogenized equation or the two-scale finite element scheme are analyzed. It is shown that the scheme provided in this article is convergent for any fixed diffusion coefficient δ, and it may be convergent independent of δ under some conditions. The numerical results
demonstrating the theoretical results are presented in this article.

Key words: Convection-diffusion problem, homogenization, micro-structure, asymptotic expansion

中图分类号: 

  • 65N30