Abstract

. The identification of discontinuous parameters in elliptic systems is formulated as a constrained minimization problem combining the output least squares and the equation error method. The minimization problem is then proved to be equivalent to the saddle-point problem of an augmented Lagrangian. The finite element method is used to discretize the saddle-point problem, and the convergence of the discretization is also proved. Finally, an Uzawa algorithm is suggested for solving the discrete saddle-point problem and is shown to be globally convergent. Key words. parameter identification, elliptic system, augmented Lagrangian, finite element method AMS subject classifications. 65N30, 35R30 PII. S0363012997318602 1. Introduction. The main purpose of this paper is to propose a numerical approach and conduct convergence analyses on each approximation process in the identification of the unknown coe#cient q in the elliptic problem -# (q#u) = f in ## u = 0 on #. The identifying process i...

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