A locking-free nonconforming FEM for optimal control problems governed by linear elasticity equations

In this paper, we investigate a locking-free nonconforming finite element method (FEM) for linear elasticity optimal control problems (OCPs) via the variational control discretization approach. Due to the fact that the finite element interpolation operator is identical to the Ritz projection, optimal error estimates are established for the control, state and adjoint state variables, respectively. Numerical experiments are also provided to validate the theoretical results.