Legendre-Fenchel duality and a generalized constitutive relation error

Mengwu Guo*, Weimin Han, Hongzhi Zhong

*Corresponding author for this work

Research output: Working paperProfessional

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.
Original languageEnglish
PublisherarXiv.org
Number of pages17
Publication statusPublished - 2016
Externally publishedYes

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