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

Wenbin Liu; Ningning Yan

doi:10.1007/s002110100380

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

Numerische Mathematik ◽

10.1007/s002110100380 ◽

2003 ◽

Vol 93 (3) ◽

pp. 497-521 ◽

Cited By ~ 84

Author(s):

Wenbin Liu ◽

Ningning Yan

Keyword(s):

Optimal Control ◽

Error Estimates ◽

Parabolic Equations ◽

Optimal Control Problems ◽

A Posteriori Error Estimates ◽

Posteriori Error ◽

Control Problems ◽

A Posteriori ◽

A Posteriori Error

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

Science in China Series A Mathematics ◽

10.1007/s11425-008-0097-9 ◽

2008 ◽

Vol 51 (8) ◽

pp. 1376-1390 ◽

Cited By ~ 14

Author(s):

YanPing Chen ◽

YunQing Huang ◽

NianYu Yi

Keyword(s):

Optimal Control ◽

Spectral Method ◽

Error Estimates ◽

Parabolic Equations ◽

Optimal Control Problems ◽

A Posteriori Error Estimates ◽

Posteriori Error ◽

Control Problems ◽

A Posteriori ◽

A Posteriori Error

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A posteriori error estimates for mixed finite element solutions of convex optimal control problems

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2006.11.015 ◽

2008 ◽

Vol 211 (1) ◽

pp. 76-89 ◽

Cited By ~ 67

Author(s):

Yanping Chen ◽

Wenbin Liu

Keyword(s):

Optimal Control ◽

Finite Element ◽

Error Estimates ◽

Optimal Control Problems ◽

Mixed Finite Element ◽

A Posteriori Error Estimates ◽

Posteriori Error ◽

Control Problems ◽

A Posteriori ◽

A Posteriori Error

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A Posteriori Error Estimates of Recovery Type for Distributed Convex Optimal Control Problems

Journal of Scientific Computing ◽

10.1007/s10915-007-9147-7 ◽

2007 ◽

Vol 33 (2) ◽

pp. 155-182 ◽

Cited By ~ 39

Author(s):

Ruo Li ◽

Wenbin Liu ◽

Ningning Yan

Keyword(s):

Optimal Control ◽

Error Estimates ◽

Optimal Control Problems ◽

A Posteriori Error Estimates ◽

Posteriori Error ◽

Control Problems ◽

A Posteriori ◽

A Posteriori Error

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A posteriori error estimates for hp finite element solutions of convex optimal control problems

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2011.02.004 ◽

2011 ◽

Vol 235 (12) ◽

pp. 3435-3454 ◽

Cited By ~ 10

Author(s):

Yanping Chen ◽

Yijie Lin

Keyword(s):

Optimal Control ◽

Finite Element ◽

Error Estimates ◽

Optimal Control Problems ◽

A Posteriori Error Estimates ◽

Posteriori Error ◽

Control Problems ◽

A Posteriori ◽

A Posteriori Error ◽

Hp Finite Element

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A posteriori error estimates for optimal control problems constrained by convection-diffusion equations

Frontiers of Mathematics in China ◽

10.1007/s11464-015-0456-0 ◽

2015 ◽

Vol 11 (1) ◽

pp. 55-75

Author(s):

Hongfei Fu ◽

Hongxing Rui ◽

Zhaojie Zhou

Keyword(s):

Optimal Control ◽

Error Estimates ◽

Optimal Control Problems ◽

A Posteriori Error Estimates ◽

Posteriori Error ◽

Diffusion Equations ◽

Control Problems ◽

A Posteriori ◽

A Posteriori Error ◽

Convection Diffusion

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A posteriori error estimates for the fractional optimal control problems

Journal of Inequalities and Applications ◽

10.1186/s13660-015-0662-z ◽

2015 ◽

Vol 2015 (1) ◽

Author(s):

Xingyang Ye ◽

Chuanju Xu

Keyword(s):

Optimal Control ◽

Error Estimates ◽

Optimal Control Problems ◽

A Posteriori Error Estimates ◽

Posteriori Error ◽

Control Problems ◽

A Posteriori ◽

A Posteriori Error ◽

Fractional Optimal Control ◽

Fractional Optimal Control Problems

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A Posteriori Error Estimates for Discontinuous Galerkin Time-Stepping Method for Optimal Control Problems Governed by Parabolic Equations

SIAM Journal on Numerical Analysis ◽

10.1137/s0036142902397090 ◽

2004 ◽

Vol 42 (3) ◽

pp. 1032-1061 ◽

Cited By ~ 43

Author(s):

Wenbin Liu ◽

Heping Ma ◽

Tao Tang ◽

Ningning Yan

Keyword(s):

Optimal Control ◽

Discontinuous Galerkin ◽

Parabolic Equations ◽

Optimal Control Problems ◽

A Posteriori Error Estimates ◽

Posteriori Error ◽

Control Problems ◽

A Posteriori ◽

A Posteriori Error ◽

Time Stepping

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A Posteriori Error Estimates of Mixed Methods for Quadratic Optimal Control Problems Governed by Parabolic Equations

Numerical Mathematics Theory Methods and Applications ◽

10.4208/nmtma.2011.m1017 ◽

2011 ◽

Vol 4 (4) ◽

pp. 439-458 ◽

Cited By ~ 2

Author(s):

Tianliang Hou

Keyword(s):

Optimal Control ◽

Mixed Methods ◽

Parabolic Equations ◽

Optimal Control Problems ◽

A Posteriori Error Estimates ◽

Posteriori Error ◽

Control Problems ◽

A Posteriori ◽

A Posteriori Error ◽

Quadratic Optimal Control

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Residual Based A Posteriori Error Estimates for Convex Optimal Control Problems Governed by Stokes-Darcy Equations

Numerical Mathematics Theory Methods and Applications ◽

10.4208/nmtma.2012.m1113 ◽

2012 ◽

Vol 5 (4) ◽

pp. 602-634 ◽

Cited By ~ 2

Author(s):

Ming Cui and Ningning Yan

Keyword(s):

Optimal Control ◽

Error Estimates ◽

Optimal Control Problems ◽

A Posteriori Error Estimates ◽

Posteriori Error ◽

Control Problems ◽

A Posteriori ◽

A Posteriori Error ◽

Darcy Equations

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A Posteriori Error Estimates of Mixed Methods for Parabolic Optimal Control Problems

Numerical Functional Analysis and Optimization ◽

10.1080/01630563.2010.492046 ◽

2010 ◽

Vol 31 (10) ◽

pp. 1135-1157 ◽

Cited By ~ 10

Author(s):

Yanping Chen ◽

Lingli Liu ◽

Zuliang Lu

Keyword(s):

Optimal Control ◽

Mixed Methods ◽

Error Estimates ◽

Optimal Control Problems ◽

A Posteriori Error Estimates ◽

Posteriori Error ◽

Control Problems ◽

A Posteriori ◽

A Posteriori Error ◽

Parabolic Optimal Control

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