PROJECTION METHOD APPLIED TO DIFFUSION IN A PERIODIC STRUCTURE.

A method designed to replace PDE's with rapidly varying coefficients by PDE's with constant coefficients is analyzed. This method is based on a combination of an asymptotic expansion and a variational principle. It is shown that for smooth data the method has the same approximation properties as the more standard approach based only on an asymptotic expansion. More important, it is shown that the present method works well also for nonsmooth data. This may be seen as a result of the optimal way in which the method treats boundary layers.