Comptes Rendus
Data completion for the Stokes system
Comptes Rendus. Mécanique, Volume 337 (2009) no. 9-10, pp. 703-708.

This Note is concerned with the severely ill-posed Cauchy–Stokes problem. This inverse problem is rephrased into an optimization one: An energy-like error functional is introduced. We prove that the optimality condition of the first order is equivalent to solving an interfacial equation which turns out to be a Cauchy–Steklov–Poincaré operator. Numerical trials highlight the efficiency of the present method.

Cette Note concerne le problème mal-posé de Cauchy–Stokes. On réécrit ce problème en terme d'optimisation d'une fonctionnelle d'erreur de type écart à la loi de comportement. La condition d'optimalité du premier ordre conduit à une équation d'interface Cauchy–Steklov–Poincaré sur la partie à compléter. Des essais numériques illustrent l'efficacité de cette méthode.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crme.2009.09.007
Keywords: Computational fluid mechanics, Cauchy–Stokes problem, Data completion, Inverse problem, Steklov–Poincaré operator
Mot clés : Mécanique des fluides numérique, Complétion de données, Opérateur de Steklov–Poincaré, Problème de Cauchy–Stokes, Problème inverse

Amel Ben Abda 1; Imen Ben Saad 1; Maatoug Hassine 1

1 LAMSIN, École nationale d'ingénieurs de Tunis, université Tunis-El Manar, B.P. 37, 1002 Le Belvédère, Tunisia
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Amel Ben Abda; Imen Ben Saad; Maatoug Hassine. Data completion for the Stokes system. Comptes Rendus. Mécanique, Volume 337 (2009) no. 9-10, pp. 703-708. doi : 10.1016/j.crme.2009.09.007. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2009.09.007/

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