Exponential decay of the resonance error in numerical homogenization via parabolic and elliptic cell problems
Numerical Analysis
2024-12-20 v1 Numerical Analysis
Abstract
This paper presents two new approaches for finding the homogenized coefficients of multiscale elliptic PDEs. Standard approaches for computing the homogenized coefficients suffer from the so-called resonance error, originating from a mismatch between the true and the computational boundary conditions. Our new methods, based on solutions of parabolic and elliptic cell-problems, result in an exponential decay of the resonance error.
Keywords
Cite
@article{arxiv.1901.09758,
title = {Exponential decay of the resonance error in numerical homogenization via parabolic and elliptic cell problems},
author = {Assyr Abdulle and Doghonay Arjmand and Edoardo Paganoni},
journal= {arXiv preprint arXiv:1901.09758},
year = {2024}
}