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

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. (C) 2003 IMACS. Published by Elsevier B.V. All rights reserved.