In this talk,
we present a general adaptive
multiscale model reduction framework, based on
the Generalized Multiscale Finite Element Method. Besides
the method's basic outline, we discuss some important ingredients
needed for the method's success.
We also discuss several applications. The proposed method allows
performing local model reduction in the presence of high contrast and no scale
separation. The research is partially supported by the Hong Kong
RGC General Research Fund (Project: 14317516).