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
Abstract
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
