An Optimal EDG Method for Distributed Control of Convection Diffusion PDEs
Provides a rigorous numerical analysis for a specific class of PDE-constrained optimization problems, but is incremental as it extends existing EDG methods to a new problem setting.
The paper proposes an embedded discontinuous Galerkin method for distributed control of convection diffusion PDEs, achieving optimal error estimates for state, dual state, fluxes, and control, and proving equivalence of optimize-then-discretize and discretize-then-optimize approaches.
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.