A finite element method for elliptic problems with rapidly oscillating coefficients

被引：0
作者：
Wen-Ming He
Jun-Zhi Cui
机构：
[1] Wenzhou University,Department of Mathematics
[2] CAS,Institute of Computational Mathematics and Scientific/Engineering Computing
来源：
BIT Numerical Mathematics | 2007年 / 47卷
关键词：
Finite Element Method; Error Estimate; Numerical Approximation; Element Solution; Nodal Point;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, we consider solving second-order elliptic problems with rapidly oscillating coefficients. Under the assumption that the oscillating coefficients are periodic, on the basis of classical homogenization theory, we present a finite element method whose key is to combine a numerical approximation of the 1-order approximate solution of those equations and a numerical approximation of the classical boundary corrector of those equations from different meshes exploiting the need for different levels of resolution. Numerical experiments are included to illustrate the competitive behavior of the proposed finite element method.
引用
收藏
页码：77 / 102
页数：25
相关论文
共 15 条
  • [1] Avellaneda M.(1989)Theory of homogenization Commun. Pure Appl. Math. 42 803-847
  • [2] Lin F.-H.(1991) bounds on singular integrals in homogenization Commun. Pure Appl. Math. 44 897-910
  • [3] Avellaneda M.(1999)Convergence of a multiscale finite element method for elliptic problem with oscillation coefficients Math. Comput. 68 913-943
  • [4] Lin F.-H.(2000)Convergence of nonconforming multiscale finite element method SIAM J. Numer. Anal. 37 888-910
  • [5] Hou Y.-Z.(1980)Smoothness properties of bounded solution of Dirichlet problem for elliptic equations in regions with corners on the boundaries Can. Math. Bull. 23 213-226
  • [6] Yalchin R.E.(2005)A pointwise estimate on the 1-order approximation of $G_{x_{0}}^{\varepsilon}$ , IMA J Appl. Math. 70 241-269
  • [7] Hou T.Y.(2005)Asymptotic expansion method for the two point boundary value problem with small periodic structure Appl. Math. Comput. 161 771-779
  • [8] Wu X.-H.(1992)Homogenization and two-scale convergence SIAM J. Math. Anal. 23 1482-1518
  • [9] Azzam A.(2006)An SQP approach with line search for a system of nonlinear equations Math. Comput. Model. 43 368-373
  • [10] He W.(undefined)undefined undefined undefined undefined-undefined
12