Error estimate and unfolding for periodic homogenization

Article type: Research Article

Authors: Griso, Georges

Affiliations: Laboratoire Jacques‐Louis Lions, CNRS & Université Pierre et Marie Curie (Paris VI), Boîte postale 187, 4, place Jussieu 75252 Paris cedex 05, France E‐mail: georges.griso@wanadoo.fr

Abstract: This paper deals with the error estimate in problems of periodic homogenization. The methods used are those of the periodic unfolding. We give the upper bound of the distance between the unfolded gradient of a function belonging to H1(Ω) and the space ∇xH1(Ω)⌖∇yL2(Ω;H1per(Y)). These distances are obtained thanks to a technical result presented in Theorem 2.3: the periodic defect of a harmonic function belonging to H1(Y) is written with the help of the norms H1/2 of its traces differences on the opposite faces of the cell Y. The error estimate is obtained without any supplementary hypothesis of regularity on correctors.

Journal: Asymptotic Analysis, vol. 40, no. 3-4, pp. 269-286, 2004