Mid Sweden University

We characterize some G-limits using two-scale techniques and investigate a method to detect deviations from the arithmetic mean in the obtained G-limit, where no peirodicity assumptions are involved. We also prove some results on the properties of generalized two-scale convergence.

We study an intermediate case between the two-scale convergence of Nguetseng and the more general concept of scale convergence of Mascarenhas and Toader. Suitable assumptions to provide scale convergence with some of the most essential properties of two-scale convergence are identified. Some aspects of the characterization of limits for sequences of gradients are discussed briefly.

This article deals with homogenization methods, namely two-scale convergence and Hconvergence, with the aim of comparing their efficiency in studying composite materials. Analytic examples are given to illustrate both methods. While compensated compactness allows one to determine the limit of a product of two weakly converging sequences under additional assumptions on the derivatives, two-scale convergence takes advantage of underlying oscillations of solution sequences and H-convergence is concerned with the operator behaviour. Special attention is paid to periodic homogenization as this case yields the most involved results. Numerical experiments are used to investigate open questions in H-convergence dealing with the possible relaxation of some convergence hypotheses. Partial results are established in this respect.