论文标题
由第二种的变异不等式控制的最佳控制问题的先验错误分析
A Priori Error Analysis for an Optimal Control Problem Governed by a Variational Inequality of the Second Kind
论文作者
论文摘要
我们考虑了第二种椭圆形变异不平等的最佳控制问题。该问题由状态的线性有限元素离散，对控件的各种离散方法。基于二次生长条件，我们得出了几乎最佳的先验误差估计。此外，我们建立了二阶足够的最佳条件，以确保二次增长条件。这些条件是相当限制的，但允许我们构建具有降低规律性的一维本地最佳解决方案，这是数值实验的精确解决方案。
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.
