A Priori Error Estimates for Space-Time Finite Element Discretization of Parabolic Optimal Control Problems Part I: Problems Without Control Constraints
A Priori Error Estimates for Space-Time Finite Element Discretization of Parabolic Optimal Control Problems Part I: Problems Without Control Constraints
复制标题
DOI：
10.1137/070694016
复制
发表时间：
2008-03
期刊：
影响因子：
--
通讯作者：
Dominik Meidner;B. Vexler
中科院分区：
文献类型：
--
作者：
Dominik Meidner;B. Vexler
本文对线性抛物型方程最优控制问题的Galerkin有限元离散进行了先验误差分析。状态变量的空间离散化采用协调元，而时间离散化采用间断伽辽金法。对于不同类型的控制离散化，我们提供的最佳顺序的误差估计空间和时间离散化参数。本文分为两个部分。在第一部分中，我们发展了一些稳定性和误差估计的时空离散的状态方程和提供误差估计的最优控制问题，没有控制约束。在本文的第二部分中，使用第一部分的技术和结果来对控制变量具有逐点不等式约束的最优控制问题进行先验误差分析。
In this paper we develop a priori error analysis for Galerkin finite element discretizations of optimal control problems governed by linear parabolic equations. The space discretization of the state variable is done using usual conforming finite elements, whereas the time discretization is based on discontinuous Galerkin methods. For different types of control discretizations we provide error estimates of optimal order with respect to both space and time discretization parameters. The paper is divided into two parts. In the first part we develop some stability and error estimates for space-time discretization of the state equation and provide error estimates for optimal control problems without control constraints. In the second part of the paper, the techniques and results of the first part are used to develop a priori error analysis for optimal control problems with pointwise inequality constraints on the control variable.