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.

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
Mots-clés : Inverse obstacle problem, acoustic waveguide, Tikhonov regularization, mixed formulation, quasi-reversibility, level set method
Bourgeois, Laurent 1 ; Recoquillay, Arnaud 1

1 
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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. http://www.numdam.org/articles/10.1051/m2an/2018008/

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