Geodesic
A mixed formulation of the Tikhonov regularization and its application to inverse PDE problems
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 52 (2018) no. 1, pp. 123-145 Cet article a éte moissonné depuis la source Numdam

Voir la notice de l'article

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.

Reçu le :
Accepté le :
DOI : 10.1051/m2an/2018008
Classification : 35J05, 35R25, 35R30, 35R35
Keywords: Inverse obstacle problem, acoustic waveguide, Tikhonov regularization, mixed formulation, quasi-reversibility, level set method 
@article{M2AN_2018__52_1_123_0,
     author = {Bourgeois, Laurent and Recoquillay, Arnaud},
     title = {A mixed formulation of the {Tikhonov} regularization and its application to inverse {PDE} problems},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {123--145},
     year = {2018},
     publisher = {EDP-Sciences},
     volume = {52},
     number = {1},
     doi = {10.1051/m2an/2018008},
     zbl = {1397.35074},
     mrnumber = {3808155},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2018008/}
}
TY  - JOUR
AU  - Bourgeois, Laurent
AU  - Recoquillay, Arnaud
TI  - A mixed formulation of the Tikhonov regularization and its application to inverse PDE problems
JO  - ESAIM: Mathematical Modelling and Numerical Analysis 
PY  - 2018
SP  - 123
EP  - 145
VL  - 52
IS  - 1
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/m2an/2018008/
DO  - 10.1051/m2an/2018008
LA  - en
ID  - M2AN_2018__52_1_123_0
ER  - 
%0 Journal Article
%A Bourgeois, Laurent
%A Recoquillay, Arnaud
%T A mixed formulation of the Tikhonov regularization and its application to inverse PDE problems
%J ESAIM: Mathematical Modelling and Numerical Analysis 
%D 2018
%P 123-145
%V 52
%N 1
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/m2an/2018008/
%R 10.1051/m2an/2018008
%G en
%F M2AN_2018__52_1_123_0
Bourgeois, Laurent; Recoquillay, Arnaud. A mixed formulation of the Tikhonov regularization and its application to inverse PDE problems. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 52 (2018) no. 1, pp. 123-145. doi: 10.1051/m2an/2018008

Cité par Sources :