Efficient numerical method for reliable upper and lower bounds on homogenized parameters
Numerical Analysis
2023-07-24 v2 Numerical Analysis
Abstract
A numerical procedure providing guaranteed two-sided bounds on the effective coefficients of elliptic partial differential operators is presented. The upper bounds are obtained in a standard manner through the variational formulation of the problem and by applying the finite element method. To obtain the lower bounds we formulate the dual variational problem and introduce appropriate approximation spaces employing the finite element method as well. We deal with the 3D setting, which has been rarely considered in the literature so far. The theoretical justification of the procedure is presented and supported with illustrative examples.
Cite
@article{arxiv.2208.09940,
title = {Efficient numerical method for reliable upper and lower bounds on homogenized parameters},
author = {Liya Gaynutdinova and Martin Ladecký and Aleš Nekvinda and Ivana Pultarová and Jan Zeman},
journal= {arXiv preprint arXiv:2208.09940},
year = {2023}
}
Comments
27 pages, 2 figures, 2 tables