Joshua Siktar - Analysis and Discretization of Optimal Control Problems in Peridynamics

In this talk, we investigate a non-local optimal control problem in solid mechanics involving a linear, bond-based peridynamics model; this model depends on the horizon parameter, which is the degree of non-locality. In addition to establishing the well-posedness of our problem, we study the behavior as the horizon parameter approaches zero. We then analyze a finite element-based discretization of this problem, its convergence, and the so-called asymptotic compatibility as the discretization parameter and the horizon parameter tend to zero simultaneously.