中文摘要：

在这份报纸，我们讨论混合不连续的 Galerkin (DG ) 有限元素近似到线性寓言的最佳的控制问题。为州的变量和有肋骨的变量，不连续的有限元素方法被用于混合的时间 discretization 和 Raviart-Thomas 有限元素方法被用于空间 discretization。我们不做 discretize 可被考虑的控制的空间，但是含蓄地利用关系在之间有肋骨并且为控制的 discretization 的控制。我们导出为最低顺序的估计混合了的一个 priori 错误 DG 有限元素近似。Moveover 为在空间和时间的任意的顺序的元素，我们导出 posteriori L2 (0， T；L2()) 为分级的功能的错误估计，假设仅仅内在的网孔是静态的。最后，我们在场在一个 priori 错误上证实理论结果的一个例子估计。[从作者抽象]

英文摘要：

In this paper, we discuss the mixed discontinuous Galerkin （DG） finite element ap- proximation to linear parabolic optimal control problems. For the state variables and the co-state variables, the discontinuous finite element method is used for the time dis- cretization and the Raviart-Thomas mixed finite element method is used for the space discretization. We do not discretize the space of admissible control but implicitly utilize the relation between co-state and control for the discretization of the control. We de- rive a priori error estimates for the lowest order mixed DG finite element approximation. Moveover, for the element of arbitrary order in space and time, we derive a posteriori L2（O, T; L2（Ω）） error estimates for the scalar functions, assuming that only the underlying mesh is static. Finally, we present an example to confirm the theoretical result on a priori error estimates.