An abstract inf-sup problem inspired by limit analysis in perfect plasticity and related applications

0545246 - ÚGN 2022 RIV SG eng J - Článek v odborném periodiku
Sysala, Stanislav - Haslinger, Jaroslav - Reddy, B. D. - Repin, S.
An abstract inf-sup problem inspired by limit analysis in perfect plasticity and related applications.
Mathematical Models and Methods in Applied Sciences. Roč. 31, č. 8 (2021), s. 1593-1623. ISSN 0218-2025. E-ISSN 1793-6314
Grant CEP: GA ČR(CZ) GA19-11441S
Institucionální podpora: RVO:68145535
Klíčová slova: convex optimization * duality * inf-sup conditions on cones * regularization * computable majorants * plasticity * delamination * limit analysis
Obor OECD: Applied mathematics
Impakt faktor: 3.803, rok: 2021
Způsob publikování: Omezený přístup
https://www.worldscientific.com/doi/10.1142/S0218202521500330

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.
Trvalý link: http://hdl.handle.net/11104/0321987