A multiscale finite element method for elliptic problems with highly oscillatory coefficients

Authors:
Jinru Chen;Junzhi Cui
Affiliations:
School of Mathematics and Comptuter Sciences, Nanjing Normal University, Nanjing, 210097, People's Republic of China;Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, P.O. Box 2719, Beijing 100080, People's Repub ...
Venue:
Applied Numerical Mathematics
Year:
2004

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Abstract

This paper is concerned with a so-called multiscale finite element method for solving elliptic problems with highly oscillatory coefficients. A special multiscale conforming finite element space, whose base functions consist of linear conforming base functions defined on a relatively coarse triangulation plus special bubble-like functions which include the small scale information, is constructed. Meanwhile the error of the multiscale finite element solution is analysed. Furthermore, a two level domain decomposition preconditioning algorithm is presented for solving the discrete problem. Finally, numerical experiments are given to show the effectiveness of our preconditioning algorithm.