ERROR ESTIMATES OF RT1 MIXED METHODS FOR DISTRIBUTED OPTIMAL CONTROL PROBLEMS

被引：2

作者：

Hou, Tianliang ^{[1
]}

机构：

[1] Chongqing Three Gorges Univ, Sch Math & Stat, Key Lab Nonlinear Sci & Syst Struct, Chongqing 404100, Peoples R China

来源：

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY | 2014年 / 51卷 / 01期

关键词：

elliptic equations; distributed optimal control problems; L-infinity-error estimates; RT1 mixed finite element methods; FINITE-ELEMENT METHODS; SUPERCONVERGENCE; APPROXIMATION;

D O I：

10.4134/BKMS.2014.51.1.139

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we investigate the error estimates of a quadratic elliptic control problem with pointwise control constraints. The state and the co-state variables are approximated by the order k = 1 Raviart-Thomas mixed finite element and the control variable is discretized by piecewise linear but discontinuous functions. Approximations of order h(3/2) in the L-2-norm and order h in the L-infinity-norm for the control variable are proved.

引用

页码：139 / 156

页数：18

共 21 条

[1] [Anonymous], 1971, OPTIMAL CONTROL SYST
[2] Error estimates for the numerical approximation of a semilinear elliptic control problem
Arada, N
Casas, E
Tröltzsch, F
[J]. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, 2002, 23 (02) : 201 - 229
[3] Adaptive finite element methods for optimal control of partial differential equations: Basic concept
Becker, R
Kapp, H
Rannacher, R
[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2000, 39 (01) : 113 - 132
[4] Brezzi F., 1991, Mixed and Hybrid Finite Element Methods, V15
[5] Superconvergence of quadratic optimal control problems by triangular mixed finite element methods
Chen, Yanping
[J]. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2008, 75 (08) : 881 - 898
[6] Superconvergence of mixed finite element methods for optimal control problems
Chen, Yanping
[J]. MATHEMATICS OF COMPUTATION, 2008, 77 (263) : 1269 - 1291
[7] A posteriori error estimates for mixed finite element solutions of convex optimal control problems
Chen, Yanping
Liu, Wenbin
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2008, 211 (01) : 76 - 89
[8] Error Estimates and Superconvergence of Mixed Finite Element Methods for Convex Optimal Control Problems
Chen, Yanping
Huang, Yunqing
Liu, Wenbin
Yan, Ningning
[J]. JOURNAL OF SCIENTIFIC COMPUTING, 2010, 42 (03) : 382 - 403
[9] Superconvergence for Optimal Control Problems Governed by Semi-linear Elliptic Equations
Chen, Yanping
Dai, Yongquan
[J]. JOURNAL OF SCIENTIFIC COMPUTING, 2009, 39 (02) : 206 - 221
[10] CIARLET P. G., 2002, Classics in Appl. Math., V40

← 1 2 3 →