A POSTERIORI ERROR ESTIMATE OF OPTIMAL CONTROL PROBLEM OF PDE WITH INTEGRAL CONSTRAINT FOR STATE

被引：21

作者：

Yuan, Lei ^{[1
]}

Yang, Danping ^{[2
]}

机构：

[1] Shandong Univ, Dept Math, Jinan 250100, Peoples R China

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

来源：

JOURNAL OF COMPUTATIONAL MATHEMATICS | 2009年 / 27卷 / 04期

关键词：

State-constrained optimal control problem; Adaptive finite element method; A posteriori error estimate; FINITE-ELEMENT APPROXIMATION; EQUATIONS;

D O I：

10.4208/jcm.2009.27.4.017

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study adaptive finite element discretization schemes for an optimal control problem governed by elliptic PDE with an integral constraint for the state. We derive the equivalent a posteriori error estimator for the finite element approximation, which particularly suits adaptive multi-meshes to capture different singularities of the control and the state. Numerical examples are presented to demonstrate the efficiency of a posteriori error estimator and to confirm the theoretical results.

引用

页码：525 / 542

页数：18

共 24 条

[1]

[Anonymous], 1971, OPTIMAL CONTROL SYST

[2]

Barbu V., 1978, CONVEXITY OPTIMIZATI

[3] Adaptive finite element methods for optimal control of partial differential equations: Basic concept [J].

Becker, R ;

Kapp, H ;

Rannacher, R .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2000, 39 (01) :113-132

[4] On the structure of Lagrange multipliers for state-constrained optimal control problems [J].

Bergounioux, M ;

Kunisch, K .

SYSTEMS & CONTROL LETTERS, 2003, 48 (3-4) :169-176

[5] General optimality conditions for constrained convex control problems [J].

Bergounioux, M ;

Tiba, D .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1996, 34 (02) :698-711

[6]

BONNAS JF, 2000, PERTURBATION ANAL OP

[7] CONTROL OF AN ELLIPTIC PROBLEM WITH POINTWISE STATE CONSTRAINTS [J].

CASAS, E .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1986, 24 (06) :1309-1318

[8]

Casas E., 2003, ESAIM P, V13, P18

[9]

Ciarlet Philippe G., 2002, Finite Element Method for Elliptic Problems

[10] Convergence of a finite element approximation to a state-constrained elliptic control problem [J].

Deckelnick, Klaus ;

Hinze, Michael .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2007, 45 (05) :1937-1953

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