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We propose an embedded discontinuous Galerkin (EDG) method to approximate thesolution of a distributed control problem governed by convection diffusionPDEs, 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 resultsconfirm our theoretical results.

An Optimal EDG Method for Distributed Control of Convection Diffusion PDEs