Circumventing the lack of dissipation in certain Oldroyd models

Vivette Girault; L. Ridgway Scott

doi:10.1016/j.crma.2017.05.013

Mathematical analysis

Circumventing the lack of dissipation in certain Oldroyd models

Presented by: Olivier Pironneau

Vivette Girault ¹; L. Ridgway Scott ²

¹ Sorbonne Universités, UPMC Université Paris-6, CNRS, UMR 7598, Laboratoire Jacques-Louis-Lions, 4, place Jussieu, 75005 Paris, France
² Departments of Computer Science and Mathematics, Computation Institute and Institute for Biophysical Dynamics, University of Chicago, Chicago, IL 60637, USA

Comptes Rendus. Mathématique, Volume 355 (2017) no. 7, pp. 753-759.

Abstract
Résumé

We modify an argument of Renardy proving existence and regularity for a subset of a class of models of non-Newtonian fluids suggested by Oldroyd, including the upper-convected and lower-convected Maxwellian models. We suggest an effective method for solving these models, which can provide a variational formulation suitable for finite element computation.

Nous modifions le raisonnement utilisé par Renardy pour prouver l'existence et la régularité de solutions d'une sous-classe de modèles de fluides non newtoniens introduits par Oldroyd, comme les modèles maxwelliens de sur-convection et sous-convection. Nous proposons une méthode itérative variationnelle de calcul de solutions qui s'adapte aux éléments finis.

Received: 2017-05-22
Accepted: 2017-05-30
Published online: 2017-06-20

DOI: 10.1016/j.crma.2017.05.013

Author's affiliations:

Vivette Girault ¹; L. Ridgway Scott ²

¹ Sorbonne Universités, UPMC Université Paris-6, CNRS, UMR 7598, Laboratoire Jacques-Louis-Lions, 4, place Jussieu, 75005 Paris, France
² Departments of Computer Science and Mathematics, Computation Institute and Institute for Biophysical Dynamics, University of Chicago, Chicago, IL 60637, USA

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     author = {Vivette Girault and L. Ridgway Scott},
     title = {Circumventing the lack of dissipation in certain {Oldroyd} models},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {753--759},
     publisher = {Elsevier},
     volume = {355},
     number = {7},
     year = {2017},
     doi = {10.1016/j.crma.2017.05.013},
     language = {en},
}

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Vivette Girault; L. Ridgway Scott. Circumventing the lack of dissipation in certain Oldroyd models. Comptes Rendus. Mathématique, Volume 355 (2017) no. 7, pp. 753-759. doi : 10.1016/j.crma.2017.05.013. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.05.013/

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