A local discontinuous Galerkin method for Dirichlet boundary control problems

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.