Volume 14, Number 3, Fall 2006
ON THE DETERMINATION OF LIMITS FOR
SOME SEQUENCES OF FUNCTIONS AND
A. HOLMBOM, M. OLSSON AND J. SILFVER
Abstract. The main concern of this paper is to study
methods to determine the effective properties of various kinds
of heterogeneous materials, and in particular to distinguish between
which disturbances that can and cannot be neglected.
In this connection we discuss limits for pairs of weakly convergent
sequences, and the relation between such limits of traditional
types and some different versions of two-scale convergence.
These ideas are applied to characterize H-limits for some
sequences of elliptic partial differential equations. Numerical
experiments are performed to investigate the process when the
determination of the limits becomes non-trivial.