A quasi-reversibility approach to solve the inverse obstacle problem

Laurent Bourgeois; Jérémi Dardé

doi:10.3934/ipi.2010.4.351

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2010, Volume 4, Issue 3: 351-377. Doi: 10.3934/ipi.2010.4.351

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A quasi-reversibility approach to solve the inverse obstacle problem

Laurent Bourgeois^1, and
Jérémi Dardé^1,

1.
Laboratoire POEMS, ENSTA, 32, Boulevard Victor, 75739 Paris Cedex 15

Received: May 2009

Revised: November 2009

Published: August 2010

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Abstract

We introduce a new approach based on the coupling of the method of quasi-reversibility and a simple level set method in order to solve the inverse obstacle problem with Dirichlet boundary condition. We provide a theoretical justification of our approach and illustrate its feasibility with the help of numerical experiments in $2D$.

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Mathematics Subject Classification: 35A15, 35N25, 35R25, 35R30,35R35, 65M60.

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