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.
@article{arxiv.1712.10106,
title = {An Optimal EDG Method for Distributed Control of Convection Diffusion PDEs},
author = {Xiao Zhang and Yangwen Zhang and John R. Singler},
journal= {arXiv preprint arXiv:1712.10106},
year = {2019}
}