6533b824fe1ef96bd127feee
RESEARCH PRODUCT
An abstract inf-sup problem inspired by limit analysis in perfect plasticity and related applications
Sergey RepinSergey RepinStanislav SysalaB. Daya ReddyJaroslav Haslingersubject
Computer scienceApplied MathematicsRegular polygonDuality (optimization)Bilinear interpolationPlasticityRegularization (mathematics)Mathematics::Numerical Analysissymbols.namesakeLimit analysisTheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITYModeling and SimulationConvex optimizationsymbolsApplied mathematicsLagrangiandescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2021-06-17 | Mathematical Models and Methods in Applied Sciences |