A PRIORI ERROR ANALYSIS FOR FINITE ELEMENT APPROXIMATION OF PARABOLIC OPTIMAL CONTROL PROBLEMS WITH POINTWISE CONTROL

被引：37

作者：

Gong, Wei ^{[1
]}

Hinze, Michael ^{[2
]}

Zhou, Zhaojie ^{[3
]}

机构：

[1] Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, LSEC, Beijing 100190, Peoples R China

[2] Univ Hamburg, D-20146 Hamburg, Germany

[3] Shandong Normal Univ, Sch Math Sci, Jinan 250014, Peoples R China

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2014年 / 52卷 / 01期

关键词：

optimal control problem; finite element method; a priori error estimate; parabolic equation; pointwise control; BOUNDARY CONTROL-PROBLEMS; STATE CONSTRAINTS; BURGERS-EQUATION; TIME; SYSTEMS; DISCRETIZATION; OPTIMIZATION;

D O I：

10.1137/110840133

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We consider finite element approximations of parabolic control problems with pointwise control. The state equation exhibits low regularity due to the control imposed pointwisely; this introduces some difficulties for both theoretical and numerical analysis. To discretize the optimal control problem we use variational discretization together with piecewise linear and continuous finite elements for the space discretization of the state, and we use the backward Euler scheme for time discretization. We prove a priori error estimates for the control, state, and adjoint state. Numerical experiments are provided which support the theoretical results.

引用

页码：97 / 119

页数：23

共 38 条

[1] CONVERGENCE OF FINITE-ELEMENT APPROXIMATIONS TO STATE CONSTRAINED CONVEX PARABOLIC BOUNDARY CONTROL-PROBLEMS [J].