| Issue |
ESAIM: M2AN
Volume 52, Number 1, January–February 2018
|
|
|---|---|---|
| Page(s) | 123 - 145 | |
| DOI | https://doi.org/10.1051/m2an/2018008 | |
| Published online | 04 May 2018 | |
A mixed formulation of the Tikhonov regularization and its application to inverse PDE problems
1
Laboratoire POEMS, UMR ENSTA/CNRS/INRIA, ENSTA ParisTech,
828 Boulevard des Maréchaux,
91120
Palaiseau, France
2
CEA, LIST,
Gif-sur-Yvette, France
* Corresponding author: laurent.bourgeois@ensta.fr
Received:
10
August
2017
Accepted:
15
January
2018
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.
Mathematics Subject Classification: 35J05 / 35R25 / 35R30 / 35R35
Key words: Inverse obstacle problem / acoustic waveguide / Tikhonov regularization / mixed formulation / quasi-reversibility / level set method
© EDP Sciences, SMAI 2018
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.