Residual-type a posteriori error analysis of HDG methods for Neumann boundary control problems

Abstract

We study a posteriori error analysis of linear-quadratic boundary control problems under bilateral box constraints on the control which acts through a Neumann-type boundary condition. We adopt the hybridizable discontinuous Galerkin method as the discretization technique, and the flux variables, the scalar variables, and the boundary trace variables are all approximated by polynomials of degree k. As for the control variable, it is discretized by the variational discretization concept. Then, an efficient and reliable a posteriori error estimator is introduced, and we prove that the error estimator provides an upper bound and a lower bound for the errors. Finally, numerical results are presented to illustrate the performance of the obtained a posteriori error estimator.