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.

我们研究了在双边箱约束下通过Neumann型边界条件作用的控制下线性-二次边界控制问题的后验误差分析。我们采用可混合的不连续Galerkin方法作为离散化技术，通量变量，标量变量和边界迹线变量均由k次多项式近似。至于控制变量，通过变分离散化概念进行离散化。然后，介绍了一种高效可靠的后验误差估计器，证明了误差估计器为误差提供了一个上界和一个下界。最后，数值结果表明所获得的后验误差估计器的性能。