Legendre-Fenchel duality and a generalized constitutive relation error
Numerical Analysis
2016-11-18 v1
Abstract
A generalized constitutive relation error is proposed in an analogous form to Fenchel-Young inequality on the basis of the key idea of Legendre-Fenchel duality theory. The generalized constitutive relation error is linked with the global errors of some admissible solutions for the problem in question, and is of wide applicability, especially in a posteriori error estimations of numerical methods. A class of elliptic variational inequalities is examined using the proposed approach and a strict upper bound of global energy errors of admissible solutions is obtained.
Cite
@article{arxiv.1611.05589,
title = {Legendre-Fenchel duality and a generalized constitutive relation error},
author = {Mengwu Guo and Weimin Han and Hongzhi Zhong},
journal= {arXiv preprint arXiv:1611.05589},
year = {2016}
}
Comments
17 pages; submitted to peer-reviewed journal