A posteriori error estimates for optimal control problems governed by parabolic equations

被引：135

作者：

Liu, WB ^{[1
]}

Yan, NN

机构：

[1] Univ Kent, CBS, Canterbury CT2 7PE, Kent, England

[2] Chinese Acad Sci, Acad Math & Syst Sci, Inst Syst Sci, Beijing, Peoples R China

来源：

NUMERISCHE MATHEMATIK | 2003年 / 93卷 / 03期

关键词：

D O I：

10.1007/s002110100380

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we derive a posteriori error estimates for the finite element approximation of quadratic optimal control problem governed by linear parabolic equation. We obtain a posteriori error estimates for both the state and the control approximation. Such estimates, which are apparently not available in the literature, are an important step towards developing reliable adaptive finite element approximation schemes for the control problem.

引用

页码：497 / 521

页数：25

共 50 条

[1] A posteriori error estimates for optimal control problems governed by parabolic equations
Wenbin Liu
Ningning Yan
[J]. Numerische Mathematik, 2003, 93 : 497 - 521
[2] A posteriori error estimates of spectral method for optimal control problems governed by parabolic equations
CHEN YanPing1
[J]. Science China Mathematics, 2008, (08) : 1376 - 1390
[3] A posteriori error estimates of spectral method for optimal control problems governed by parabolic equations
YanPing Chen
YunQing Huang
NianYu Yi
[J]. Science in China Series A: Mathematics, 2008, 51 : 1376 - 1390
[4] A posteriori error estimates of spectral method for optimal control problems governed by parabolic equations
Chen YanPing
Huang YunQing
Yi NianYu
[J]. SCIENCE IN CHINA SERIES A-MATHEMATICS, 2008, 51 (08): : 1376 - 1390
[5] A Posteriori Error Estimates of Mixed Methods for Quadratic Optimal Control Problems Governed by Parabolic Equations
Hou, Tianliang
Chen, Yanping
Huang, Yunqing
[J]. NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS, 2011, 4 (04) : 439 - 458
[6] A New A Posteriori Error Estimates for Optimal Control Problems Governed by Parabolic Integro-Differential Equations
H. Chen
T. Hou
[J]. Numerical Analysis and Applications, 2024, 17 : 67 - 79
[7] A New A Posteriori Error Estimates for Optimal Control Problems Governed by Parabolic Integro-Differential Equations
Chen, H.
Hou, T.
[J]. NUMERICAL ANALYSIS AND APPLICATIONS, 2024, 17 (01) : 67 - 79
[8] EQUIVALENT A POSTERIORI ERROR ESTIMATES FOR A CONSTRAINED OPTIMAL CONTROL PROBLEM GOVERNED BY PARABOLIC EQUATIONS
Sun, Tongjun
Ge, Liang
Liu, Wenbin
[J]. INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING, 2013, 10 (01) : 1 - 23
[9] Local a posteriori error estimates for boundary control problems governed by nonlinear parabolic equations
Manohar, Ram
Sinha, Rajen Kumar
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2022, 409
[10] A posteriori error estimates for control problems governed by Stokes equations
Liu, WB
Yan, NN
[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 2002, 40 (05) : 1850 - 1869

← 1 2 3 4 5 →