Comptes Rendus
A numerical method to solve the Stokes problem with a punctual force in source term
Comptes Rendus. Mécanique, Volume 343 (2015) no. 3, pp. 187-191.

The aim of this note is to present a numerical method to solve the Stokes problem in a bounded domain with a Dirac source term, which preserves optimality for any approximation order by the finite-element method. It is based on the knowledge of a fundamental solution to the associated operator over the whole space. This method is motivated by the modeling of the movement of active thin structures in a viscous fluid.

Le but de cette note est de présenter une méthode numérique pour la résolution du problème de Stokes avec une force ponctuelle en terme source, qui assure l'optimalité de l'erreur d'approximation éléments finis. Elle s'appuie sur la connaissance explicite d'une solution fondamentale de l'opérateur linéaire associé. Cette méthode est motivée par la modélisation du mouvement de structures fines actives dans un fluide visqueux.

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Accepted:
Published online:
DOI: 10.1016/j.crme.2014.09.008
Keywords: Error estimates, Finite element method, Stokeslet, Thin structures
Mot clés : Estimations d'erreur, Méthode éléments finis, Stokeslet, Structures fines

Loïc Lacouture 1

1 Université Paris-Sud, Laboratoire de Mathématiques d'Orsay, CNRS UMR 8628, Faculté des sciences d'Orsay, bâtiment 425, 91405 Orsay cedex, France
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Loïc Lacouture. A numerical method to solve the Stokes problem with a punctual force in source term. Comptes Rendus. Mécanique, Volume 343 (2015) no. 3, pp. 187-191. doi : 10.1016/j.crme.2014.09.008. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2014.09.008/

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