L^q -regularization for the inverse Robin problem

Abstract

In this paper, an inverse Robin problem for an elliptic equation is investigated. The Robin coe cient is assumed to be a small perturbation from a reference coe cient, hence a sparse structure is a priori known. An -regularized output least square formulation is considered with ∈ (0, 1). The existence of the minimizer is proved. The convergence of the nite element discretization with respect to mesh size is shown. A modi ed Newton algorithm is applied to solve the smoothing rst order optimality system. Two-dimensional and threedimensional numerical examples demonstrate the e ciency of the proposed method.

Sparse optimization problems in fractional order Sobolev spaces

“…Another motivation is the study of sparse source or coefficient identification problems, see, e.g. [6,15,24]. In order to avoid over-smoothing, we study the regularization in H s (Ω) for small s ∈ (0, 1).…”