The main aim of this article is to analyze mixed finite element method for the second order Dirichlet boundary control problem. Therein, we develop both a priori and a posteriori error analysis using the energy space based approach. We obtain optimal order a priori error estimates in the energy norm and $L^2$-norm with the help of auxiliary problems. The reliability and the efficiency of proposed a posteriori error estimator is discussed using the Helmholtz decomposition. Numerical experiments are presented to confirm the theoretical findings.

翻译：本条的主要目的是为第二顺序Drichlet边界控制问题分析混合限定要素方法。 因此,我们利用以能源空间为基础的方法,进行先验和事后误差分析,在辅助问题的帮助下,在能源规范中取得最优的先验误差估计,在次要问题的帮助下获得2美元以诺尔姆为单位的先验误差估计,在使用Helmholtz分解法的情况下,讨论拟议的后验误差估测器的可靠性和效率。提出数字实验,以证实理论结论。