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

摘要

A method based on an augmented Lagrangian formulation is developed which allows one to estimate coefficients in an elliptic differential equation 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. (KR)