FINITE ELEMENT APPROXIMATIONS OF AN OPTIMAL CONTROL PROBLEM WITH INTEGRAL STATE CONSTRAINT

被引：54

作者：

Liu, Wenbin ^{[1
,2
]}

Yang, Danping ^{[3
]}

Yuan, Lei ^{[4
]}

Ma, Chaoqun ^{[1
]}

机构：

[1] Hunan Univ, Sch Business Adm, Changsha 410082, Hunan, Peoples R China

[2] Univ Kent, KBS, Canterbury CT2 7PE, Kent, England

[3] E China Normal Univ, Dept Math, Shanghai 200241, Peoples R China

[4] SW Forest Univ, Dept Fundamental Courses, Kunming 650224, Yunnan, Peoples R China

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2010年 / 48卷 / 03期

关键词：

optimal control problem; integral state constraint; finite element approximation; gradient projection algorithm; a priori error estimate; ELLIPTIC CONTROL-PROBLEM; MESHES;

D O I：

10.1137/080737095

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

An integral state-constrained optimal control problem governed by an elliptic partial differential equation and its finite element approximation are considered. The finite element approximation is constructed on multimeshes. An L-2-norm a priori error estimate of the finite element approximation is obtained. Further, some superconvergence results are proved. Based on these superconvergence results, almost optimal L-infinity-norm error estimates are derived. Some recovery algorithms are then proposed to produce a posteriori error estimators of gradient type. To solve the finite element system, a simple and yet efficient iterative gradient projection algorithm is proposed and its convergence rate is proved. Some numerical examples are performed to confirm theoretical analysis.

引用

页码：1163 / 1185

页数：23

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