An equation error approach for the identification of elastic parameters in beams and plates with H1 regularization

Abstract

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 H1 regularization whereas other optimization-based formulations commonly use H2 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.