Year: 2008
Type: conference-paper
Abstract: We use the Lavrentiev method for the regularization of the severely ill-posed data completion problem, put under a variational Steklov-Poincare form. In the choice of the regularizing parameter, we check a ' super-optimal ' a priori convergence criterion. Consequently, the solutions obtained by the regularization provide a minimizing sequence of the Kohn-Vogelius function, with a ' quadratic ' decaying of the minimum value of it toward zero, instead of the linear rate predicted by the general theory. We call such a result the ' super-convergence' of the approximated 'incompatibility measure ' of the variational problem. Finally, we apply the a posteriori Morozov discrepancy principle to the Kohn-Vogelius functional and show how it yields a regularizing strategy. We achieve by some numerical illustrations to support our analysis.
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W1996347641