An Optimal EDG Method for Distributed Control of Convection Diffusion PDEs

TL;DR

This paper introduces an embedded discontinuous Galerkin method for distributed control of convection diffusion PDEs, providing optimal error estimates and confirming the equivalence of optimization approaches through numerical validation.

Contribution

The paper develops an EDG method with proven optimal error bounds for convection diffusion control problems and demonstrates the equivalence of OD and DO approaches.

Findings

Optimal a priori error estimates achieved.

Numerical results confirm theoretical predictions.

OD and DO approaches are shown to coincide.

Abstract

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.