Error control based model reduction for multiscale problems

Abstract

In this contribution we review a posteriori based discretization methods for variational multiscale problems  and suggest a suitable conceptual approach for an ecient numerical treatment of parametrized variational  multiscale problems where the parameters are either chosen from a low dimensional parameter space or  consists of parameter functions from some compact low dimensional manifold that is embedded in some  high dimensional or even innite dimensional function space. The approach is based on combinations of ideas  from established numerical multiscale methods and ecient model reduction approaches such as the reduced  basis method.