SUMMARYWe restrict the variational multiscale method to a class of methods we denote by numerical multiscale methods. Numerical multiscale methods are methods obtained by enriching the piecewise linear functions with special local functions. The enrichment provides additional stabilization via terms obtained by static condensation. The resulting methods are improvements of the coarse scale solutions by the approximations of the fine scales emanating from the enrichments.Copyright © 2011 John Wiley & Sons, Ltd.