论文标题
半跟踪半线性椭圆方程的最佳控制问题的错误估计值
Error estimates for a pointwise tracking optimal control problem of a semilinear elliptic equation
论文作者
论文摘要
我们考虑了半椭圆形偏微分方程的最佳跟踪最佳控制问题。我们得出了最佳解决方案的存在，并首先分析了必要和足够的二阶最优条件。我们设计了两种离散化策略，以近似最佳控制问题的解决方案：一个半分化方案，其中控制变量未离散 - 所谓的变分离散化方法 - 以及一个完全离散的方案，其中控制变量通过分段恒定恒定功能离散。对于两种解决方案技术，我们分析离散化的收敛性能并得出误差估计。
We consider a pointwise tracking optimal control problem for a semilinear elliptic partial differential equation. We derive the existence of optimal solutions and analyze first and, necessary and sufficient, second order optimality conditions. We devise two strategies of discretization to approximate a solution of the optimal control problem: a semidiscrete scheme where the control variable is not discretized -- the so-called variational discretization approach -- and a fully discrete scheme where the control variable is discretized with piecewise constant functions. For both solution techniques, we analyze convergence properties of discretizations and derive error estimates.
