An Equation Error Approach for the Identification of Elastic Parameters in Beams and Plates with H_1 Regularization

摘要

In this short note deals with the nonlinear inverse problem of identifying a variable parameter in fourth-order partial differential equations using an equation error approach. These equations arise in several important applications such as car windscreen modeling, deformation of plates, etc. To counter the highly ill-posed nature of the considered inverse problem, a regularization must be performed. The main contribution of this work is to show that the equation error approach permits the use of H~1 regularization whereas other optimization-based formulations commonly use H_2 regularization. We give the existence and convergence results for the equation error formulation. An illustrative numerical example is given to show the feasibility of the approach.