Numerical homogenization and correctors for nonlinear elliptic equations

Y. Efendiev*, A. Pankov

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

21 Scopus citations

Abstract

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 languageEnglish (US)
Pages (from-to)43-68
Number of pages26
JournalSIAM Journal on Applied Mathematics
Volume65
Issue number1
DOIs
StatePublished - 2005
Externally publishedYes

Keywords

  • Elliptic
  • Finite element
  • Homogenization
  • Multiscale
  • Nonlinear
  • Random
  • Scale-up
  • Upscaling

ASJC Scopus subject areas

  • Applied Mathematics

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