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Licensed Unlicensed Requires Authentication Published by De Gruyter May 21, 2015

Incorporating a posteriori error estimators in an adaptive parametrization algorithm

  • Hend Ben Ameur EMAIL logo , Nizar Kharrat and Zoubida Mghazli


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.

The authors would like to thank Professor Frederic Hecht for his help and advices when using Freefem++ for the numerical tests.

Received: 2014-12-19
Revised: 2015-2-13
Accepted: 2015-2-26
Published Online: 2015-5-21
Published in Print: 2016-6-1

© 2016 by De Gruyter

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