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Reconstructing initial data using observers: error analysis of the semi-discrete and fully discrete approximations

Haine, Ghislain and Ramdani, Karim Reconstructing initial data using observers: error analysis of the semi-discrete and fully discrete approximations. (2012) Numerische Mathematik, 120 (2). 307-343. ISSN 0029-599X

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Official URL: http://dx.doi.org/10.1007/s00211-011-0408-x

Abstract

A new iterative algorithm for solving initial data inverse problems from partial observations has been recently proposed in Ramdani et al. (Automatica 46(10), 1616-1625, 2010 ). Based on the concept of observers (also called Luenberger observers), this algorithm covers a large class of abstract evolution PDE's. In this paper, we are concerned with the convergence analysis of this algorithm. More precisely, we provide a complete numerical analysis for semi-discrete (in space) and fully discrete approximations derived using finite elements in space and an implicit Euler method in time. The analysis is carried out for abstract Schrödinger and wave conservative systems with bounded observation (locally distributed).

Item Type:Article
Additional Information:Thanks to Springer editor. The definitive version is available at http://www.springerlink.com The original PDF of the article can be found at Numerische Mathematik website: http://link.springer.com/journal/211
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Institut National de la Recherche en Informatique et en Automatique - INRIA (FRANCE)
Other partners > Université Henri Poincaré-Nancy1 - UHP (FRANCE)
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Deposited By: Ghislain Haine
Deposited On:27 Jun 2013 14:59

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