论文标题
最佳控制问题的时空有限元离散化的先验误差估计，该问题由耦合线性PDE-ODE系统控制
A priori error estimates for the space-time finite element discretization of an optimal control problem governed by a coupled linear PDE-ODE system
论文作者
论文摘要
在本文中，我们研究了由简化的线性梯度增强损伤模型控制的最佳控制问题的时空盖尔金有限元离散化的先验误差估计。模型方程是特殊的结构，因为状态方程由椭圆PDE组成，该椭圆形几乎必须在几乎所有时间与必须在空间中几乎所有点中保持真实的ODE结合在一起。该状态方程在时间上通过分段常数不连续的Galerkin方法离散，并且通常在空间中符合线性有限元。对于控制的离散化，我们采用了相同的离散技术，事实证明，该技术等同于各种离散化方法。我们为状态方程的离散以及最佳控制提供了最佳顺序的错误估计。添加数值实验以说明促成的收敛速率。
In this paper we investigate a priori error estimates for the space-time Galerkin finite element discretization of an optimal control problem governed by a simplified linear gradient enhanced damage model. The model equations are of a special structure as the state equation consists of an elliptic PDE which has to be fulfilled at almost all times coupled with an ODE that has to hold true in almost all points in space. The state equation is discretized by a piecewise constant discontinuous Galerkin method in time and usual conforming linear finite elements in space. For the discretization of the control we employ the same discretization technique which turns out to be equivalent to a variational discretization approach. We provide error estimates of optimal order both for the discretization of the state equation as well as for the optimal control. Numerical experiments are added to illustrate the proven rates of convergence.
