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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

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Volume 24, Issue 3


Incorporating a posteriori error estimators in an adaptive parametrization algorithm

Hend Ben Ameur / Nizar Kharrat / Zoubida Mghazli
Published Online: 2015-05-21 | DOI: https://doi.org/10.1515/jiip-2014-0088


We are interested on an inverse problem of distributed parameter estimation in a partial differential equation (PDE) from measures of the PDE's solution. The considered parameter is supposed to be a piecewise constant function. Identifying the parameterization consists on identifying both values of the parameter and shapes of zones where the parameter is constant. We develop a posteriori error estimators for the considered inverse problem and we present a new algorithm, result of the combination between adaptive parameterization technique, leading to overcome the underdetermination problem and, an adaptive mesh technique, guided by a posteriori error estimators, providing more precise results.

Keywords: Inverse problem; parameter estimation; adaptive parametrization; error estimators

MSC: 35R30; 49N45; 65D15; 65N15

About the article

Received: 2014-12-19

Revised: 2015-02-13

Accepted: 2015-02-26

Published Online: 2015-05-21

Published in Print: 2016-06-01

Citation Information: Journal of Inverse and Ill-posed Problems, Volume 24, Issue 3, Pages 293–308, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jiip-2014-0088.

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