  This paper analyzes an interface-unfitted numerical method for distributed
optimal control problems governed by elliptic interface equations. We follow
the variational discretization concept to discretize the optimal control
problems, and apply a Nitsche-eXtended finite element method to discretize the
corresponding state and adjoint equations, where piecewise cut basis functions
around the interface are enriched into the standard linear element space.
Optimal error estimates of the state, co-state and control in a mesh-dependent
norm and the $L^2$ norm are derived. Numerical results are provided to verify
the theoretical results.
