A mixed formulation of the Tikhonov regularization and its application to inverse PDE problems - INRIA - Institut National de Recherche en Informatique et en Automatique Accéder directement au contenu
Article Dans Une Revue ESAIM: Mathematical Modelling and Numerical Analysis Année : 2018

A mixed formulation of the Tikhonov regularization and its application to inverse PDE problems

Résumé

This paper is dedicated to a new way of presenting the Tikhonov regularization in the form of a mixed formulation. Such formulation is well adapted to the regularization of linear ill-posed partial differential equations because when it comes to discretization, the mixed formulation enables us to use some standard finite elements. As an application of our theory, we consider an inverse obstacle problem in an acoustic waveguide. In order to solve it we use the so-called “exterior approach”, which couples the mixed formulation of Tikhonov regularization and a level set method. Some 2d numerical experiments show the feasibility of our approach.
Fichier principal
Vignette du fichier
m2an170141.pdf (2.13 Mo) Télécharger le fichier
Origine : Publication financée par une institution
Loading...

Dates et versions

hal-02922747 , version 1 (26-08-2020)

Identifiants

Citer

Laurent Bourgeois, Arnaud Recoquillay. A mixed formulation of the Tikhonov regularization and its application to inverse PDE problems. ESAIM: Mathematical Modelling and Numerical Analysis, 2018, 52 (1), pp.123-145. ⟨10.1051/m2an/2018008⟩. ⟨hal-02922747⟩
184 Consultations
308 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More