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November  2008, 2(4): 411-426. doi: 10.3934/ipi.2008.2.411

Missing boundary data reconstruction via an approximate optimal control

Rajae Aboulaϊch 1, , Amel Ben Abda 2, and  Moez Kallel 3,

1. 

Ecole Mohammadia d’Ingénieurs, LERMA, Avenue Ibn Sina, BP 765, Agdal-Rabat, Morocco
2. 

Ecole Nationale d’Ingénieurs de Tunis, LAMSIN, BP 37, 1002 Tunis Belvédère, Tunisia
3. 

Institut Préparatoire aux Etudes d’Ingénieur de Tunis & ENIT-LAMSIN, BP 37, 1002 Tunis Belvédère, Tunisia

Received  December 2007 Revised  July 2008 Published  November 2008

An approximate optimal control formulation of the Cauchy problem for elliptic equations is considered. A cost functional adding a fading through the iterations regularizing term borrowed from the domain decomposition communauty is proposed. Convergence of the descretized finite elements solution to the continuous one is proved. Numerical experiments involving smooth, non-smooth geometries as well as anisotropy highlight the capability of the present missing boundary data recovering process.
Keywords: Cauchy problem, regularization, optimal control, inverse problem.
Mathematics Subject Classification: Primary: 35J20, 49J20; Secondary: 74S05.
Citation: Rajae Aboulaϊch, Amel Ben Abda, Moez Kallel. Missing boundary data reconstruction via an approximate optimal control. Inverse Problems and Imaging, 2008, 2 (4) : 411-426. doi: 10.3934/ipi.2008.2.411
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