On an extension of the method of two-scale convergence and its applications

259 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Resolvent Estimates for High-Contrast Elliptic Problems with Periodic Coefficients (2014, background): “In Section 9 we calculate the limit of the spectra of the operators −div ( Aε(·/ε)∇ ) and explain its relation to an earlier study of [13].”
Towards a two-scale calculus (2006, background): “[2, 5, 8, 13, 17, 20, 21, 26, 35, 36], just to mention some papers of a growing literature.”
Higher order asymptotic homogenization and wave propagation in periodic composite materials (2008, background): “Non-local phenomena resulting from a high contrast (or anisotropy) of composite structures were studied by Allaire (1992), Zhikov (2000) and Cherednichenko et al. (2006).”
Analysis of the heterogeneous multiscale method for elliptic homogenization problems (2004, methodology): “[26, 35] use multiscale test functions of the form φ(x, x/ε) where φ(x, y) is periodic in y to extract the leading order behavior of u(x), extending an idea that was used analytically in the work of [2, 16, 30, 40] for the homogenization problems.”