This paper develops and analyses numerical approximation for linear-quadratic
optimal control problems governed by elliptic interface equations. We adopt variational
discretization concept to discretize optimal control problems, and apply an interfaceunfitted finite element method due to [A. Hansbo and P. Hansbo. An unfitted finite
element method, based on Nitsche’s method, for elliptic interface problems. Comput.
Methods Appl. Mech. Engrg., 191(47-48): 5537-5552, 2002] to discretize the corresponding state and adjoint equations, where piecewise cut basis functions around interface are enriched into standard conforming finite element space. Optimal error estimates in both L2 norm and a mesh-dependent norm are derived for the optimal state,
co-state and control under different regularity assumptions. Numerical results verify the