Special Session 169: Inverse problems arising in partial differential equations and mathematical physics

Regularization and discretization in the reconstruction for elliptic inverse problems
Luca Rondi
Universit\`a degli Studi di Pavia
Italy
Co-Author(s):    
Abstract:
We consider elliptic inverse problems such as the electrical impedance tomography or the determination of inhomogeneities by scattering measurements. We employ a variational approach for the reconstruction. Due to severe ill-posedness, it is needed to add to our minimization problem a regularization, for example of Tikhonov-type. The discretization used for the numerical implementation may also be another important cause of instability, which is often overlooked. We investigate how to handle simultaneously the regularization and the discretization so that the solution to the corresponding regularized and discrete minimization problem is a good approximation of the solution to the inverse problem.