Identifying Parameters in Parabolic

In this paper, we investigate the nite element method for numerically identifying physical parameters in parabolic initial-boundary value problems. The identifying problem is rst formulated as a constrained minimization problem using the output least squares approach with the H 1-regularization or BV-regularization. Then a simple nite 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 eeciency of the proposed method, even for identifying highly discontinuous and oscillated parameters.