标题： 一类由椭圆变分不等式控制的最优分布控制问题的数值分析 显示英文标题

标题： Numerical analysis of a family of optimal distributed control problems governed by an elliptic variational inequality

摘要： 一族由椭圆变分不等式（带有参数$\alpha >0$）控制的分布混合最优控制问题的数值分析通过有限元方法获得，当其参数为$h\rightarrow 0$时。 我们还获得了当$\alpha\rightarrow \infty$（对于每个$h>0$）时离散最优控制和相关状态系统解的极限，并且当$h\rightarrow 0$和$\alpha\rightarrow \infty$时得到了两个连续和两个离散最优控制及其相关状态系统解的交换图。 此外，当$(h, \alpha)\rightarrow(0, \infty)$时也获得了双重收敛性。 显示英文摘要

摘要： The numerical analysis of a family of distributed mixed optimal control problems governed by elliptic variational inequalities (with parameter $\alpha >0$) is obtained through the finite element method when its parameter $h\rightarrow 0$. We also obtain the limit of the discrete optimal control and the associated state system solutions when $\alpha\rightarrow \infty$ (for each $h>0$) and a commutative diagram for two continuous and two discrete optimal control and its associated state system solutions is obtained when $h\rightarrow 0$ and $\alpha\rightarrow \infty$. Moreover, the double convergence is also obtained when $(h, \alpha)\rightarrow(0, \infty)$.