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

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.