Numerical Analysis of Inverse Elasticity Problem with Signorini's Condition (Communications in Computational Physics, 2018)
An optimal control problem is considered to find a stable surface traction,which minimizes the discrepancy between a given displacement field and its estimation.Firstly, the inverse elastic problem is constructed by variational inequalities, anda stable approximation of surface traction is obtained with Tikhonov regularization.Then a finite element discretization of the inverse elastic problem is analyzed. Moreover,the error estimation of the numerical solutions is deduced. Finally, a numericalalgorithm is detailed and three examples in two-dimensional case illustrate the efficiency of the algorithm.