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arXiv · 2601.18969

A Local Discontinuous Galerkin Method for Dirichlet Boundary Control Problems

Peter Benner·Michael Hinze·Hamdullah Yücel
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Abstract

In this paper, we consider control constrained $L^2-$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.

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Peter Benner, Michael Hinze, Hamdullah Yücel. 2026-01-26. A Local Discontinuous Galerkin Method for Dirichlet Boundary Control Problems. https://arxiv.org/abs/2601.18969

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