An analysis of a class of variational multiscale methods based on subspace decomposition
Abstract
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.
Cite
@article{arxiv.1608.04081,
title = {An analysis of a class of variational multiscale methods based on subspace decomposition},
author = {Ralf Kornhuber and Daniel Peterseim and Harry Yserentant},
journal= {arXiv preprint arXiv:1608.04081},
year = {2018}
}
Comments
published electronically in Mathematics of Computation on January 19, 2018