A three-field augmented Lagrangian formulation of unilateral contact problems with cohesive forces
| Autor: | Alexandre Ern, Serge Piperno, David Doyen |
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| Rok vydání: | 2010 |
| Předmět: |
Numerical Analysis
Mathematical optimization Augmented Lagrangian method Applied Mathematics Numerical analysis Unilateral contact Basis function Finite element method Computational Mathematics symbols.namesake Modeling and Simulation Lagrange multiplier Collocation method symbols Applied mathematics Newton's method Analysis Mathematics |
| Zdroj: | ESAIM: Mathematical Modelling and Numerical Analysis. 44:323-346 |
| ISSN: | 1290-3841 0764-583X |
| DOI: | 10.1051/m2an/2010004 |
| Popis: | We investigate unilateral contact problems with cohesive forces, leading to the constrained minimization of a possibly nonconvex functional. We analyze the mathematical structure of the mini- mization problem. The problem is reformulated in terms of a three-field augmented Lagrangian, and sufficient conditions for the existence of a local saddle-point are derived. Then, we derive and ana- lyze mixed finite element approximations to the stationarity conditions of the three-field augmented Lagrangian. The finite element spaces for the bulk displacement and the Lagrange multiplier must satisfy a discrete inf-sup condition, while discontinuous finite element spaces spanned by nodal basis functions are considered for the unilateral contact variable so as to use collocation methods. Two iter- ative algorithms are presented and analyzed, namely an Uzawa-type method within a decomposition- coordination approach and a nonsmooth Newton's method. Finally, numerical results illustrating the theoretical analysis are presented. |
| Databáze: | OpenAIRE |
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