A Numerical Study of an Augmented Lagrangian Method for the Estimation of Parameters in Elliptic Systems

Abstract
A method based on an augmented Lagrangian formulation is developed which allows coefficients in an elliptic differential equation to be estimated from measurements of the state. This is a hybrid method combining the output-least-squares and the equation-error technique. Seminorm regularization is employed, and convergence and stability properties are discussed. Several aspects of an efficient implementation are described. Finally, the effectiveness of the method is demonstrated by means of one-and two-dimensional examples.