Abstract
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.
© 2016 by De Gruyter
