A1 Journal article (refereed)
An abstract inf-sup problem inspired by limit analysis in perfect plasticity and related applications (2021)

Sysala, S., Haslinger, J., Reddy, B. D., & Repin, S. (2021). An abstract inf-sup problem inspired by limit analysis in perfect plasticity and related applications. Mathematical Models and Methods in Applied Sciences, 31(8), 1593-1623. https://doi.org/10.1142/s0218202521500330

JYU authors or editors

Publication details

All authors or editors: Sysala, Stanislav; Haslinger, Jaroslav; Reddy, B. Daya; Repin, Sergey

Journal or series: Mathematical Models and Methods in Applied Sciences

ISSN: 0218-2025

eISSN: 1793-6314

Publication year: 2021

Publication date: 17/06/2021

Volume: 31

Issue number: 8

Pages range: 1593-1623

Publisher: World Scientific Pub Co Pte Lt

Publication country: Singapore

Publication language: English

DOI: https://doi.org/10.1142/s0218202521500330

Publication open access: Not open

Publication channel open access:

Web address of parallel published publication (pre-print): https://arxiv.org/abs/2009.03535


This paper is concerned with an abstract inf-sup problem generated by a bilinear Lagrangian and convex constraints. We study the conditions that guarantee no gap between the inf-sup and related sup-inf problems. The key assumption introduced in the paper generalizes the well-known Babuška–Brezzi condition. It is based on an inf-sup condition defined for convex cones in function spaces. We also apply a regularization method convenient for solving the inf-sup problem and derive a computable majorant of the critical (inf-sup) value, which can be used in a posteriori error analysis of numerical results. Results obtained for the abstract problem are applied to continuum mechanics. In particular, examples of limit load problems and similar ones arising in classical plasticity, gradient plasticity and delamination are introduced.

Keywords: mathematical models; plasticity; mathematical optimisation; control theory; numerical analysis; error analysis

Free keywords: convex optimization; duality; inf-sup conditions on cones; regularization; computable majorants; delamination; limit analysis

Contributing organizations

Ministry reporting: Yes

Reporting Year: 2021

JUFO rating: 2

Last updated on 2022-19-08 at 19:40