L∞-ESTIMATES OF MIXED FINITE ELEMENT METHODS FOR GENERAL NONLINEAR OPTIMAL CONTROL PROBLEMS

被引：0

作者：

Chen, Yanping ^{[1
]}

Lu, Zuliang ^{[2
,3
]}

机构：

[1] S China Normal Univ, Sch Math Sci, Guangzhou 510631, Guangdong, Peoples R China

[2] Chongqing Three Gorges Univ, Sch Math & Stat, Chongqing 404000, Peoples R China

[3] Xiangtan Univ, Coll Civil Engn & Mech, Xiangtan 411105, Peoples R China

来源：

JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY | 2012年 / 25卷 / 01期

基金：

美国国家科学基金会; 中国博士后科学基金;

关键词：

L-infinity-error estimates; mixed finite element methods; nonlinear elliptic equations; optimal; control problems; pointwise control constraints; NUMERICAL APPROXIMATION; SUPERCONVERGENCE;

D O I：

10.1007/s11424-011-9215-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper investigates L-infinity-estimates for the general optimal control problems governed by two-dimensional nonlinear elliptic equations with pointwise control constraints using mixed finite element methods. The state and the co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise constant functions. The authors derive L-infinity-estirnates for the mixed finite element approximation of nonlinear optimal control problems. Finally, the numerical examples are given.

引用

页码：105 / 120

页数：16

共 31 条

[1] Error estimates for the numerical approximation of a semilinear elliptic control problem [J].

Arada, N ;

Casas, E ;

Tröltzsch, F .

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, 2002, 23 (02) :201-229

[2]

Babuska I., 2001, NUMER MATH SCI COMP

[3] Second-order analysis for control constrained optimal control problems of semilinear elliptic systems [J].

Bonnans, JF .

APPLIED MATHEMATICS AND OPTIMIZATION, 1998, 38 (03) :303-325

[4]

BREZZI F, 1974, REV FR AUTOMAT INFOR, V8, P129

[5]

Brezzi F., 1991, Mixed and Hybrid Finite Element Methods, V15

[6] Error estimates for the numerical approximation of boundary semilinear elliptic control problems [J].

Casas, E ;

Mateos, M ;

Tröltzsch, F .

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, 2005, 31 (02) :193-219

[7] Superconvergence of mixed finite element methods for optimal control problems [J].

Chen, Yanping .

MATHEMATICS OF COMPUTATION, 2008, 77 (263) :1269-1291

[8]

Chen YP, 2006, INT J NUMER ANAL MOD, V3, P311

[9] Error estimates for parabolic optimal control problem by fully discrete mixed finite element methods [J].

Chen, Yanping ;

Lu, Zuliang .

FINITE ELEMENTS IN ANALYSIS AND DESIGN, 2010, 46 (11) :957-965

[10] Error estimates of fully discrete mixed finite element methods for semilinear quadratic parabolic optimal control problem [J].

Chen, Yanping ;

Lu, Zuliang .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2010, 199 (23-24) :1415-1423

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