The Morozov's principle applied to data assimilation problems - ENSTA Paris - École nationale supérieure de techniques avancées Paris Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2021

The Morozov's principle applied to data assimilation problems

Résumé

This paper is focused on the Morozov's principle applied to an abstract data assimilation framework, with particular attention to three simple examples: the data assimilation problem for the Laplace equation, the Cauchy problem for the Laplace equation and the data assimilation problem for the heat equation. Those ill-posed problems are regularized with the help of a mixed type formulation which is proved to be equivalent to a Tikhonov regularization applied to a well-chosen operator. The main issue is that such operator may not have a dense range, which makes it necessary to extend well-known results related to the Morozov's choice of the regularization parameter to that unusual situation. The solution which satisfies the Morozov's principle is computed with the help of the duality in optimization, possibly by forcing the solution to satisfy given a priori constraints. Some numerical results in two dimensions are proposed in the case of the data assimilation problem for the Laplace equation.
Fichier principal
Vignette du fichier
BoDa21_hal.pdf (4.26 Mo) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03344087 , version 1 (14-09-2021)
hal-03344087 , version 2 (14-02-2022)
hal-03344087 , version 3 (07-06-2022)

Identifiants

  • HAL Id : hal-03344087 , version 1

Citer

Laurent Bourgeois, Jérémi Dardé. The Morozov's principle applied to data assimilation problems. 2021. ⟨hal-03344087v1⟩
327 Consultations
181 Téléchargements

Partager

Gmail Facebook X LinkedIn More