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.

Abstract. In this paper, we study some efficient numerical methods for parameter identifications in elliptic systems. The proposed numerical methods are conducted iteratively and each iteration involves only solving positive definite linear algebraic systems, although the original inverse problems are ill-posed and highly nonlinear. The positive definite systems can be naturally preconditioned with their corresponding block diagonal matrices. Numerical experiments are presented to illustrate the efficiency of the proposed algorithms.

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