An analysis of a class of variational multiscale methods based on subspace decomposition

摘要

Numerical homogenization tries to approximate the solutions of ellipticpartial differential equations with strongly oscillating coefficients byfunctions from modified finite element spaces. We present in this paper a classof such methods that are very closely related to the method of M{\aa}lqvist andPeterseim [Math. Comp. 83, 2014]. Like the method of M{\aa}lqvist andPeterseim, these methods do not make explicit or implicit use of a scaleseparation. Their compared to that in the work of M{\aa}lqvist and Peterseimstrongly simplified analysis is based on a reformulation of their method interms of variational multiscale methods and on the theory of iterative methods,more precisely, of additive Schwarz or subspace decomposition methods.