Numerical identification of a Robin coefficient in parabolic problems (Q2894512)

The authors study a regularization approach for an inverse problem arising from transient convective heat transfer. The inverse problem in this case is to identify the space and temperature dependent Robin coefficient from noisy measurements of the temperature and flux on a part of the boundary. This paper is an extension of the authors' previous works in the stationary counterpart of the problem.NEWLINENEWLINEIn Section 2, the inverse problem is formulated as an optimization problem of minimizing a certain functional. The authors show that the forward map is well defined and go on to prove continuity and differentiability properties of the map. In Section 3, the authors propose a regularization formulation of Tikhonov type for the minimization problem, establish its well-posedness, and derive the optimality system. The existence of an optimal solution is also shown in this section. In Section 4, the authors describe a finite element discretization of the constrained optimization problem and carry out a convergence analysis. In the final section, numerical results for several one and two dimensional problems are presented in order to illustrate the accuracy and efficiency of the proposed approach. Minimization problems are solved by the conjugate gradient method with smoothed gradient.