In this paper, we consider control constrained L2−Dirichlet boundary control of a convection-diffusion equation on a two dimensional convex polygonal domain. We discretize the control problem based on the local discontinuous Galerkin method with piecewise linear ansatz functions for the flux and potential. We derive a priori error estimates for the full as well as for the variational discrete control approximation. We present a selection of numerical results to demonstrate the performance of our approach and to underpin the theoretical findings.
@article{arxiv.2601.18969,
title = {A Local Discontinuous Galerkin Method for Dirichlet Boundary Control Problems},
author = {Peter Benner and Michael Hinze and Hamdullah Yücel},
journal= {arXiv preprint arXiv:2601.18969},
year = {2026}
}