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

Jérémi Dardé | Zendy; Laurent Bourgeois | Zendy

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

Author(s) -

Jérémi Dardé,

Laurent Bourgeois

Publication year - 2014

Publication title -

inverse problems and imaging

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.755

H-Index - 40

eISSN - 1930-8345

pISSN - 1930-8337

DOI - 10.3934/ipi.2014.8.23

Subject(s) - obstacle , mathematics , mathematical proof , stokes flow , boundary (topology) , convergence (economics) , set (abstract data type) , boundary value problem , obstacle problem , coupling (piping) , inverse , mathematical analysis , inverse problem , flow (mathematics) , computer science , geometry , political science , law , economics , programming language , economic growth , mechanical engineering , engineering

International audienceWe 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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