In this paper we consider numerical homogenization and correctors for nonlinear elliptic equations. The numerical correctors are constructed for operators with homogeneous random coefficients. The construction employs two scales, one a physical scale and the other a numerical scale. A numerical homogenization technique is proposed and analyzed. This procedure is developed within finite element formulation. The convergence of the numerical procedure is presented for the case of general heterogeneities using G-convergence theory. The proposed numerical homogenization procedure for elliptic equations can be considered as a generalization of multiscale finite element methods to nonlinear equations. Using corrector results we construct an approximation of oscillatory solutions. Numerical examples are presented.
|Original language||English (US)|
|Number of pages||26|
|Journal||SIAM Journal on Applied Mathematics|
|State||Published - 2005|
- Finite element
ASJC Scopus subject areas
- Applied Mathematics