Higher Order Triangular Mixed Finite Element Methods for Semi linear Quadratic Optimal Control Problems

被引：5

作者：

Deng, Kang ^{[2
]}

Chen, Yanping ^{[1
]}

Lu, Zuliang ^{[3
,4
]}

机构：

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

[2] Hunan Univ Sci & Technol, Sch Math Sci, Xiangtan 411201, Peoples R China

[3] Chongqing Three Gorges Univ, Coll Math & Comp Sci, Chongqing 404000, Peoples R China

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

来源：

NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS | 2011年 / 4卷 / 02期

基金：

美国国家科学基金会;

关键词：

a priori error estimates; semilinear optimal control problems; higher order triangular elements; mixed finite element methods; APPROXIMATION; SUPERCONVERGENCE;

D O I：

10.4208/nmtma.2011.42s.4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we investigate a priori error estimates for the quadratic optimal control problems governed by semilinear elliptic partial differential equations using higher order triangular mixed finite element methods. The state and the co-state are approximated by the order k Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise polynomials of order k (k >= 0). A priori error estimates for the mixed finite element approximation of semilinear control problems are obtained. Finally, we present some numerical examples which confirm our theoretical results.

引用

页码：180 / 196

页数：17

共 26 条

[1]

[Anonymous], 1977, Grundlagen der mathematischen Wissenschaften

[2]

[Anonymous], 1971, OPTIMAL CONTROL SYST

[3] 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

[4]

Babuska I., 2001, NUMER MATH SCI COMP

[5] 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

[6]

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

[7]

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

[8] Superconvergence of quadratic optimal control problems by triangular mixed finite element methods [J].

Chen, Yanping .

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2008, 75 (08) :881-898

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

Chen, Yanping .

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

[10]

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

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