An analysis of a class of variational multiscale methods based on subspace decomposition
Ralf Kornhuber, Daniel Peterseim, Harry Yserentant · Mathematics of Computation · 2017
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 a class of such methods that are closely related to the methods that have recently been proposed by Målqvist and Peterseim [Math. Comp. 83, 2014, pp. 2583–2603]. Like these methods, the new methods do not make explicit or implicit use of a scale separation. Their comparatively simple analysis is based on the theory of additive Schwarz or subspace decomposition methods.