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I am writing a paper in which I want to cite the earliest reference to the augmented Lagrangian method in FEM. For the pure Lagrangian method in FEM, the classical work of Babuška [1] is the original paper, but I cannot find it for the augmented Lagrangian technique.

[1] Babuška, I. The finite element method with Lagrangian multipliers. Numerische Mathematik, 20(3):179–192, 1973.

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  • $\begingroup$ Well, if you haven't seen the reference before it means it has not influenced your work, why citing it? $\endgroup$ – nicoguaro Jul 9 at 13:40
  • $\begingroup$ In fact, it's a PhD thesis and the review chapter compares several constraint enforcement methods (Lagrange multiplier, augmented Lagrange multiplier, penalty, Nitsche, etc.) in FEM. For the other methods I could find the original references; I thought it would be nice if I could also do it for the augmented Lagrangian method). $\endgroup$ – Zoltán Csáti Jul 9 at 14:04
  • $\begingroup$ Have you checked the following? (1) Glowinski, Roland, and A. Marroco. "Sur l'approximation, par éléments finis d'ordre un, et la résolution, par pénalisation-dualité d'une classe de problèmes de Dirichlet non linéaires." ESAIM: Mathematical Modelling and Numerical Analysis-Modélisation Mathématique et Analyse Numérique 9.R2 (1975): 41-76. (2) Gabay, Daniel, and Bertrand Mercier. A dual algorithm for the solution of non linear variational problems via finite element approximation. Institut de recherche d'informatique et d'automatique, 1975. $\endgroup$ – nicoguaro Jul 9 at 18:30
  • $\begingroup$ Neither of them. I will check them in the upcoming days and tell my opinion. Thanks for the references. $\endgroup$ – Zoltán Csáti Jul 9 at 19:01
  • $\begingroup$ @nicoguaro The first reference, from Glowinski, is the one I need. If you write it to an answer, I will accept it. $\endgroup$ – Zoltán Csáti Jul 15 at 14:48
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I have found the following two references:

  1. Glowinski, Roland, and A. Marroco. Sur l'approximation, par éléments finis d'ordre un, et la résolution, par pénalisation-dualité d'une classe de problèmes de Dirichlet non linéaires. ESAIM: Mathematical Modelling and Numerical Analysis-Modélisation Mathématique et Analyse Numérique 9.R2 (1975): 41-76.

  2. Gabay, Daniel, and Bertrand Mercier. A dual algorithm for the solution of non linear variational problems via finite element approximation. Institut de recherche d'informatique et d'automatique, 1975.

After the OP reviewed the references it appears that 1. Glowinski and Marroco 1975 is the first one discussing the topic.

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