An extension of the stochastic two-scale convergence method and application

Article type: Research Article

Authors: Heida, Martin

Affiliations: Institute for Applied Mathematics, University of Heidelberg, Im Neuenheimer Feld 294, 69120 Heidelberg, Germany. Tel.: +49 6221 546223; E-mail: [email protected]

Abstract: The stochastic two-scale convergence method, recently developed in an article by Zhikov and Piatnitskii [Izv. Math. 70(1) (2006), 19–67] is extended to arbitrary probability spaces and is now based on the theory of stochastic geometry instead of random measures. It will be shown that former results on stochastic and periodic two-scale convergence fit into the new approach in a natural way. These results will be applied to functions with jumps on (n−1)-dimensional manifolds, in particular to a homogenization problem of heat transfer through a composite material or polycrystal.

Keywords: stochastic homogenization, two-scale convergence, singular structures, heat transfer

DOI: 10.3233/ASY-2010-1022

Journal: Asymptotic Analysis, vol. 72, no. 1-2, pp. 1-30, 2011