Numerical identifications of parameters in parabolic systems

Abstract

. In this paper, we investigate the numerical identifications of physical parameters in parabolic initial-boundary value problems. The identifying problem is first formulated as a constrained minimization one using the output least squares approach with the H 1 -regularization or BV -regularization. Then a simple finite element method is used to approximate the constrained minimization problem and the convergence of the approximation is shown for both regularizations. The discrete constrained problem can be reduced to a sequence of unconstrained minimization problems. Numerical experiments are presented to show the efficiency of the proposed method, even for identifying highly discontinuous and oscillating parameters. 1. Introduction In this paper, we consider a finite element approach, combined with the output least squares method, for identifying the parameter q(x) in the following parabolic problem #u #t - # (q(x)#u) = f (x, t ) in # (0, T ) (1.1) with the initial condition ...