We consider an optimal control problem governed by an elliptic variational inequality of the second kind. The problem is discretized by linear finite elements for the state and a variational discrete approach for the control. Based on a quadratic growth condition we derive nearly optimal a priori error estimates. Moreover, we establish second order sufficient optimality conditions that ensure a quadratic growth condition. These conditions are rather restrictive, but allow us to construct a one-dimensional locally optimal solution with reduced regularity, which serves as an exact solution for numerical experiments.

中文翻译：

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第二类变分不等式最优控制问题的先验误差分析

我们考虑由第二种椭圆变分不等式控制的最优控制问题。通过状态的线性有限元和控制的变分离散方法将问题离散化。基于二次增长条件，我们得出了几乎最佳的先验误差估计。此外，我们建立了确保二次增长条件的二阶充分最优条件。这些条件是限制性的，但是允许我们构造具有减小的规则性的一维局部最优解，这可以作为数值实验的精确解。