In this paper, we revisit the $L_2$-norm error estimate for $C^0$-interior penalty analysis of Dirichlet boundary control problem governed by biharmonic operator. In this work, we have relaxed the interior angle condition of the domain from $120$ degrees to $180$ degrees, therefore this analysis can be carried out for any convex domain. The theoretical findings are illustrated by numerical experiments. Moreover, we propose a new analysis to derive the error estimates for the biharmonic equation with Cahn-Hilliard type boundary condition under minimal regularity assumption.

翻译：在本文中,我们重新审视了对双声管操作员管理的迪里切莱边界控制问题进行内部处罚分析的2美元以内值为单位的误差估计值,在这项工作中,我们已经将域内角条件从120美元度放宽为180美元度,因此可以对任何曲线领域进行这种分析,用数字实验来说明理论结论。此外,我们提议进行新的分析,根据最低常规假设,得出带有卡恩-希利亚德型边界条件的双声调方程的误差估计值。