  A homogenization approach is one of effective strategies to solve multiscale
elliptic problems approximately. The finite element heterogeneous multiscale
method (FEHMM) which is based on the finite element makes possible to simulate
such process numerically. In this paper we introduce a FEHMM scheme for
multiscale elliptic problems based on nonconforming spaces. In particular we
use the noconforming element with the periodic boundary condition introduced in
the companion paper. Theoretical analysis derives a priori error estimates in
the standard Sobolev norms. Several numerical results which confirm our
analysis are provided.
