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

被引：0

作者：

吴志华

严宁宁

机构：

[1] Institute of System Sciences Academy of Mathematics and System Sciences Chinese Academy of Sciences

[2] Beijing 100080

[3] China

来源：

ActaMathematicaScientia | 2008年 / 02期

关键词：

Convection-diffusion problem; homogenization; micro-structure; asymptotic expansion;

D O I：

暂无

中图分类号：

O241.82 [偏微分方程的数值解法];

学科分类号：

070102 ;

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 coefficientδ,and it may be convergent inde- pendent ofδunder some conditions.The numerical results demonstrating the theoretical results are presented in this article.

引用

页码：236 / 252

页数：17

共 13 条

[1]

Lecture Notes in Computational Science and Engineering. Brandt A. Springer . 2002

[2]

Time Scales in Homogenization of Periodic Flows with Vanishing Molecular Diffusion. Albert Fannjiang. Journal of Differential Equations . 2002

[3] BOUNDARY-LAYERS IN LINEAR ELLIPTIC SINGULAR PERTURBATION PROBLEMS [J].

ECKHAUS, W .

SIAM REVIEW, 1972, 14 (02) :225-&

[4]

The heterogeneous multi-scale methods. E W,Engquist B. Computation Materials Science .

[5]

Boundary layers in linear elliptic singular perturbation problems. Eckhaus W. SIAM Review . 1972

[6]

Mathematical Problems in Elasticity and Homogenization. Oleinik O A, Shamaev A S, Yosifan G A. North-Holland . 1992

[7]

A multiscale finite element method for elliptic problems in composite materials and porous media. Hou T, Wu X. Journal of Computational Physics . 1997

[8]

Homogenization and its applications. Babu■ka I. SYNSPADE . 1975

[9]

The Finite Element Method for Elliptic Problems. Ciarlet PG. North-Holland . 1978

[10]

A uniform convergent Galerkin method on a Shishkin mesh for a convection- diffusion problem. Stynes M,O‘Riordan E. Journal of Mathematical Analysis and Applications . 1997

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