Numerical homogenization and correctors for nonlinear elliptic equations Academic Article

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. 2004 Society for Industrial and Applied Mathematics.

authors

• Efendiev, Yalchin

published proceedings

• SIAM JOURNAL ON APPLIED MATHEMATICS

author list (cited authors)

• Efendiev, Y., & Pankov, A.

citation count

• 21

complete list of authors

• Efendiev, Y||Pankov, A

publication date

• January 2004

publisher

• Society for Industrial & Applied Mathematics (SIAM)  Publisher

published in

• SIAM Journal on Applied Mathematics  Journal

keywords

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

Digital Object Identifier (DOI)

• 10.1137/S0036139903424886

URI

• https://hdl.handle.net/1969.1/178671

start page

• 43

end page

• 68

volume

• 65

issue

• 1

URL

• http://dx.doi.org/10.1137/s0036139903424886