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

Ralf Kornhuber, Harry Yserentant

Published 2016-08-14Version 1

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