In this paper, an abstract framework for the error analysis of discontinuous finite element method is developed for the distributed and Neumann boundary control problems governed by the stationary Stokes equation with control constraints. {\it A~priori} error estimates of optimal order are derived for velocity and pressure in the energy norm and the $L^2$-norm, respectively. Moreover, a reliable and efficient {\it a~posteriori} error estimator is derived. The results are applicable to a variety of problems just under the minimal regularity possessed by the well-posedness of the problem. In particular, we consider the abstract results with suitable stable pairs of velocity and pressure spaces like as the lowest-order Crouzeix-Raviart finite element and piecewise constant spaces, piecewise linear and constant finite element spaces. The theoretical results are illustrated by the numerical experiments.

翻译：在本文中,为分布式和Neumann边界控制问题开发了一个用于分析不连续有限要素方法错误的抽象框架,这些问题是由固定式斯托克斯方程式和受控制制约的边界控制问题处理的。在能源规范中,最佳顺序的误差估计分别针对速度和压力得出,而在能源规范中,最佳顺序的误差估计为$L$2美元-诺尔姆得出。此外,还产生了一个可靠和高效的误差估测器。结果适用于在问题稳妥性所具备的最低限度规律下的各种问题。特别是,我们考虑的是具有像最低级Crouzix-Raviart定点元素和小节常态常态常态空间、小道线和常态定点空间等合适的稳定速度和压力空间的抽象结果。理论结果由数字实验来说明。