Details

Autor(en) / Beteiligte

• ALLAIRE, G

Titel

Homogenization and two-scale convergence

Ist Teil von

• SIAM journal on mathematical analysis, 1992-11, Vol.23 (6), p.1482-1518

Ort / Verlag

Philadelphia, PA: Society for Industrial and Applied Mathematics

Erscheinungsjahr

1992

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• Following an idea of G. Nguetseng, the author defines a notion of "two-scale" convergence, which is aimed at a better description of sequences of oscillating functions. Bounded sequences in $L^2 (\Omega )$ are proven to be relatively compact with respect to this new type of convergence. A corrector-type theorem (i.e., which permits, in some cases, replacing a sequence by its "two-scale" limit, up to a strongly convergent remainder in $L^2 (\Omega )$) is also established. These results are especially useful for the homogenization of partial differential equations with periodically oscillating coefficients. In particular, a new method for proving the convergence of homogenization processes is proposed, which is an alternative to the so-called energy method of Tartar. The power and simplicity of the two-scale convergence method is demonstrated on several examples, including the homogenization of both linear and nonlinear second-order elliptic equations.