  We propose an embedded discontinuous Galerkin (EDG) method to approximate the
solution of a distributed control problem governed by convection diffusion
PDEs, and obtain optimal a priori error estimates for the state, dual state,
their fluxes, and the control. Moreover, we prove the optimize-then-discretize
(OD) and discrtize-then-optimize (DO) approaches coincide. Numerical results
confirm our theoretical results.
