Summary: We study the variational discretization for a constrained optimal control problem governed by convection dominated diffusion equations, where the state equation is approximated by the edge stabilization Galerkin method. A priori error estimates are derived for the state, the adjoint state and the control. Moreover, residual type a posteriori error estimates in the \(L^2\)-norm are obtained. Finally, two numerical experiments are presented to illustrate the theoretical results.