An HDG Method for Distributed Control of Convection Diffusion PDEs

TL;DR

This paper introduces an HDG method for solving distributed optimal control problems governed by convection-diffusion PDEs, providing theoretical error estimates and validating them through numerical experiments in 2D and 3D.

Contribution

The paper develops a novel HDG approach with proven optimal error estimates for convection-diffusion control problems, supported by numerical validation.

Findings

Optimal a priori error estimates derived for all variables

Numerical experiments confirm theoretical convergence rates

Method effectively handles 2D and 3D problems

Abstract

We propose a hybridizable discontinuous Galerkin (HDG) method to approximate the solution of a distributed optimal control problem governed by an elliptic convection diffusion PDE. We derive optimal a priori error estimates for the state, adjoint state, their fluxes, and the optimal control. We present 2D and 3D numerical experiments to illustrate our theoretical results.