Primal–dual formulation for parameter estimation in elastic contact problem with friction

Abstract

This work deals with a saddle point formulation of parameter identification in linear elastic contact problems with friction. Using the primal–dual formulation of the constrained minimization problem and given observations, we estimate the Lamé coefficients through the penalization and dualization of the considered inverse problem. By Fenchel duality, we provide the dual energy function associated with the constraint. We prove the existence of a solution to the regularized parameter identification problem as well as the convergence of the penalized problem to the original one. An augmented Lagrangian formulation of the inverse problem and the existence of its saddle point are provided. By means of the alternating direction method of multipliers (ADMM) and a primal–dual active set strategy (PDAS), we solve the problem numerically and illustrate our approach.

Keywords

• Inverse problem
• identification
• saddle point
• Fenchel duality
• linear elasticity
• contact problem