  Multiperforated plates exhibit high gradients and a loss of regularity
concentrated in a boundary layer for which a direct numerical simulation
becomes very expensive. For elliptic equations the solution at some distance of
the boundary is only affected in an effective way and the macroscopic and
mesoscopic behaviour can be separated. A multiscale formulation in the spirit
of the heterogeneous multiscale method is introduced on the example of the
Poisson equation. Based on the method of matched asymptotic expansion the
solution is separated into a macroscopic far field defined in a domain with
only slowly varying boundary and a mesoscopic near field defined in scaled
coordinates on possibly varying infinite periodicity cells. The near field has
a polynomial behaviour that is coupled to the traces of the macroscopic
variable on the mid-line of the multiperforated plate. A variational
formulation using a Beppo-Levi space in the strip is introduced and its
well-posedness is shown. The variational framework when truncating the infinite
strip is discussed and the truncation error is estimated.
