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The "exterior approach" to solve the inverse obstacle problem for the Stokes system

Laurent Bourgeois 1 Jérémi Dardé 1, 2
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : We apply an "exterior approach" based on the coupling of a method of quasi-reversibility and of a level set method in order to recover a fixed obstacle immersed in a Stokes flow from boundary measurements. Concerning the method of quasi-reversibility, two new mixed formulations are introduced in order to solve the ill-posed Cauchy problems for the Stokes system by using some classical conforming infite elements. We provide some proofs for the convergence of the quasi-reversibility methods on the one hand and of the level set method on the other hand. Some numerical experiments in 2D show the effciency of the two mixed formulations and of the exterior approach based on one of them.
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https://hal.inria.fr/hal-00937768
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Submitted on : Tuesday, January 28, 2014 - 6:06:04 PM
Last modification on : Thursday, January 14, 2021 - 11:56:03 AM

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Laurent Bourgeois, Jérémi Dardé. The "exterior approach" to solve the inverse obstacle problem for the Stokes system. Inverse Problems and Imaging , AIMS American Institute of Mathematical Sciences, 2014, pp.Pages: 23 - 51. ⟨10.3934/ipi.2014.8.23⟩. ⟨hal-00937768⟩

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