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## On the approximation of the solution of an optimal control problem governed by an elliptic equation

RAIRO. Anal. numér., 13 4 (1979) 313-328
Published online: 2017-02-01

## Variational discretization for optimal control problems governed by parabolic equations

Yanping Chen, Tianliang Hou and Nianyu Yi
Journal of Systems Science and Complexity 26 (6) 902 (2013)
DOI: 10.1007/s11424-013-1166-x

## Mass Lumping for the Optimal Control of Elliptic Partial Differential Equations

Arnd Rösch and Gerd Wachsmuth
SIAM Journal on Numerical Analysis 55 (3) 1412 (2017)
DOI: 10.1137/16M1074473

## Error analysis for optimal control problem governed by convection diffusion equations: DG method

Chunguang Xiong and Yuan Li
Journal of Computational and Applied Mathematics 235 (10) 3163 (2011)
DOI: 10.1016/j.cam.2010.12.024

## A Posteriori Error Estimates for Convex Boundary Control Problems

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SIAM Journal on Numerical Analysis 39 (1) 73 (2001)
DOI: 10.1137/S0036142999352187

## L∞-error estimates of higher order mixed finite element approximations for elliptic optimal control problems

Tianliang Hou
International Journal of Computer Mathematics 89 (16) 2224 (2012)
DOI: 10.1080/00207160.2012.704993

## Impulse and Sampled-Data Optimal Control of Heat Equations, and Error Estimates

Emmanuel Trélat, Lijuan Wang and Yubiao Zhang
SIAM Journal on Control and Optimization 54 (5) 2787 (2016)
DOI: 10.1137/15M1040670

## New a posteriori error estimates for hp version of finite element methods of nonlinear parabolic optimal control problems

Zuliang Lu, Hongyan Liu, Chunjuan Hou and Longzhou Cao
Journal of Inequalities and Applications 2016 (1) (2016)
DOI: 10.1186/s13660-016-0994-3

## On stabilized mixed methods for generalized Stokes problem based on the velocity–pseudostress formulation: A priori error estimates

Tomás P. Barrios, Rommel Bustinza, Galina C. García and Erwin Hernández
Computer Methods in Applied Mechanics and Engineering 237-240 78 (2012)
DOI: 10.1016/j.cma.2012.05.006

## Superconvergence of triangular Raviart–Thomas mixed finite element methods for a bilinear constrained optimal control problem

Yanping Chen, Zuliang Lu and Yunqing Huang
Computers & Mathematics with Applications 66 (8) 1498 (2013)
DOI: 10.1016/j.camwa.2013.08.019

## Error estimates of triangular mixed finite element methods for quasilinear optimal control problems

Yanping Chen, Zuliang Lu and Ruyi Guo
Frontiers of Mathematics in China 7 (3) 397 (2012)
DOI: 10.1007/s11464-012-0179-4

## Mimetic Discretizations of Elliptic Control Problems

Paola F. Antonietti, Nadia Bigoni and Marco Verani
Journal of Scientific Computing 56 (1) 14 (2013)
DOI: 10.1007/s10915-012-9659-7

## Error estimates of mixed finite element methods for quadratic optimal control problems

Xiaoqing Xing, Yanping Chen and Nianyu Yi
Journal of Computational and Applied Mathematics 233 (8) 1812 (2010)
DOI: 10.1016/j.cam.2009.09.018

## Weak boundary penalization for Dirichlet boundary control problems governed by elliptic equations

Lili Chang, Wei Gong and Ningning Yan
Journal of Mathematical Analysis and Applications 453 (1) 529 (2017)
DOI: 10.1016/j.jmaa.2017.04.016

## L ∞-estimates of mixed finite element methods for general nonlinear optimal control problems

Yanping Chen and Zuliang Lu
Journal of Systems Science and Complexity 25 (1) 105 (2012)
DOI: 10.1007/s11424-011-9215-9

## A general theorem on error estimates with application to a quasilinear elliptic optimal control problem

Eduardo Casas and Fredi Tröltzsch
Computational Optimization and Applications 53 (1) 173 (2012)
DOI: 10.1007/s10589-011-9453-8

## Error Estimates for the Numerical Approximation of Dirichlet Boundary Control for Semilinear Elliptic Equations

Eduardo Casas and Jean‐Pierre Raymond
SIAM Journal on Control and Optimization 45 (5) 1586 (2006)
DOI: 10.1137/050626600

## Numerical analysis for the approximation of optimal control problems with pointwise observations

Lili Chang, Wei Gong and Ningning Yan
Mathematical Methods in the Applied Sciences 38 (18) 4502 (2015)
DOI: 10.1002/mma.2861

## Mimetic finite differences for nonlinear and control problems

P. F. Antonietti, L. Beirão da Veiga, N. Bigoni and M. Verani
Mathematical Models and Methods in Applied Sciences 24 (08) 1457 (2014)
DOI: 10.1142/S0218202514400016

## Residual-based a posteriori error estimates for hp finite element solutions of semilinear Neumann boundary optimal control problems

Zuliang Lu, Shuhua Zhang, Chuanjuan Hou and Hongyan Liu
Boundary Value Problems 2016 (1) (2016)
DOI: 10.1186/s13661-016-0562-2

## Superconvergence of triangular mixed finite elements for optimal control problems with an integral constraint

Jianwei Zhou, Yanping Chen and Yongquan Dai
Applied Mathematics and Computation 217 (5) 2057 (2010)
DOI: 10.1016/j.amc.2010.07.006

## Adaptive Mixed Finite Element Methods for Parabolic Optimal Control Problems

Zuliang Lu
Mathematical Problems in Engineering 2011 1 (2011)
DOI: 10.1155/2011/217493

## Robust error estimates for the finite element approximation of elliptic optimal control problems

Wei Gong and Ningning Yan
Journal of Computational and Applied Mathematics 236 (6) 1370 (2011)
DOI: 10.1016/j.cam.2011.09.001

## Numerical methods for nonlinear inverse problems

T. Kärkkäinen, P. Neittaanmäki and A. Niemistö
Journal of Computational and Applied Mathematics 74 (1-2) 231 (1996)
DOI: 10.1016/0377-0427(96)00026-X

## Superconvergence of RT1 mixed finite element approximations for elliptic control problems

TianLiang Hou and YanPing Chen
Science China Mathematics 56 (2) 267 (2013)
DOI: 10.1007/s11425-012-4461-4

## A Priori Error Estimate of Splitting Positive Definite Mixed Finite Element Method for Parabolic Optimal Control Problems

Hongfei Fu, Hongxing Rui, Jiansong Zhang and Hui Guo
Numerical Mathematics: Theory, Methods and Applications 9 (02) 215 (2016)
DOI: 10.4208/nmtma.2016.m1409

## Mixed Finite Element Method for Dirichlet Boundary Control Problem Governed by Elliptic PDEs

Wei Gong and Ningning Yan
SIAM Journal on Control and Optimization 49 (3) 984 (2011)
DOI: 10.1137/100795632

## Adaptive Semidiscrete Finite Element Methods for Semilinear Parabolic Integrodifferential Optimal Control Problem with Control Constraint

Zuliang Lu
Journal of Applied Mathematics 2013 1 (2013)
DOI: 10.1155/2013/302935

## Finite element error estimates for Neumann boundary control problems on graded meshes

Thomas Apel, Johannes Pfefferer and Arnd Rösch
Computational Optimization and Applications 52 (1) 3 (2012)
DOI: 10.1007/s10589-011-9427-x

## Optimal Control of the Stokes Equations: A Priori Error Analysis for Finite Element Discretization with Postprocessing

Arnd Rösch and Boris Vexler
SIAM Journal on Numerical Analysis 44 (5) 1903 (2006)
DOI: 10.1137/050637364

## Adaptive Finite Element Approximation for Distributed Elliptic Optimal Control Problems

Ruo Li, Wenbin Liu, Heping Ma and Tao Tang
SIAM Journal on Control and Optimization 41 (5) 1321 (2002)
DOI: 10.1137/S0363012901389342

## A posteriori error estimates for some model boundary control problems

Wenbin Liu and Ningning Yan
Journal of Computational and Applied Mathematics 120 (1-2) 159 (2000)
DOI: 10.1016/S0377-0427(00)00308-3

## AC0interior penalty method for the Dirichlet control problem governed by biharmonic operator

Sudipto Chowdhury and Thirupathi Gudi
Journal of Computational and Applied Mathematics 317 290 (2017)
DOI: 10.1016/j.cam.2016.12.005

## Finite Element Method and A Priori Error Estimates for Dirichlet Boundary Control Problems Governed by Parabolic PDEs

Wei Gong, Michael Hinze and Zhaojie Zhou
Journal of Scientific Computing 66 (3) 941 (2016)
DOI: 10.1007/s10915-015-0051-2

## A priori error estimates for the finite element discretization of optimal distributed control problems governed by the biharmonic operator

S. Frei, R. Rannacher and W. Wollner
Calcolo 50 (3) 165 (2013)
DOI: 10.1007/s10092-012-0063-3

## A two-phase strategy for control constrained elliptic optimal control problems

Xiao-Liang Song and Bo Yu
Numerical Linear Algebra with Applications 25 (4) e2138 (2018)
DOI: 10.1002/nla.2138

## An efficient duality-based approach for PDE-constrained sparse optimization

Xiaoliang Song, Bo Chen and Bo Yu
Computational Optimization and Applications 69 (2) 461 (2018)
DOI: 10.1007/s10589-017-9951-4

## Error Estimates and Superconvergence of Mixed Finite Element Methods for Convex Optimal Control Problems

Yanping Chen, Yunqing Huang, Wenbin Liu and Ningning Yan
Journal of Scientific Computing 42 (3) 382 (2010)
DOI: 10.1007/s10915-009-9327-8

## Finite element methods for elliptic optimal control problems with boundary observations

Ming Yan, Wei Gong and Ningning Yan
Applied Numerical Mathematics 90 190 (2015)
DOI: 10.1016/j.apnum.2014.11.011

## Quasi-best approximation in optimization with PDE constraints

Fernando Gaspoz, Christian Kreuzer, Andreas Veeser and Winnifried Wollner
Inverse Problems 36 (1) 014004 (2020)
DOI: 10.1088/1361-6420/ab47f3

## Superconvergence of Mixed Methods for Optimal Control Problems Governed by Parabolic Equations

Xiaoqing Xing and Yanping Chen
Advances in Applied Mathematics and Mechanics 3 (4) 401 (2011)
DOI: 10.4208/aamm.10-m1006

## A posteriori error estimates of finite element methods for nonlinear quadratic boundary optimal control problem

Z. Lu
Numerical Analysis and Applications 4 (3) 210 (2011)
DOI: 10.1134/S1995423911030037

## A SUPERCONVERGENT L∞-ERROR ESTIMATE OF RT1 MIXED METHODS FOR ELLIPTIC CONTROL PROBLEMS WITH AN INTEGRAL CONSTRAINT

Yuelong Tang and Yuchun Hua
Journal of Applied Analysis & Computation 7 (3) 1037 (2017)
DOI: 10.11948/2017065

## Finite element approximation for a class of parameter estimation problems

Yanzhen Chang and Danping Yang
Journal of Systems Science and Complexity 27 (5) 866 (2014)
DOI: 10.1007/s11424-014-1218-x

## Convergence and superconvergence of variational discretization for parabolic bilinear optimization problems

Yuelong Tang and Yuchun Hua
Journal of Inequalities and Applications 2019 (1) (2019)
DOI: 10.1186/s13660-019-2195-3

## A priori error analysis for optimal distributed control problem governed by the first order linear hyperbolic equation: hp-streamline diffusion discontinuous galerkin method

Chunguang Xiong, Fusheng Luo, Xiuling Ma and Yu’an Li
Journal of Numerical Mathematics 24 (2) (2016)
DOI: 10.1515/jnma-2014-0049

## A Multilevel Correction Method for Optimal Controls of Elliptic Equations

Wei Gong, Hehu Xie and Ningning Yan
SIAM Journal on Scientific Computing 37 (5) A2198 (2015)
DOI: 10.1137/140990255

## Legendre–Galerkin spectral methods for optimal control problems with integral constraint for state in one dimension

Jianwei Zhou and Danping Yang
Computational Optimization and Applications 61 (1) 135 (2015)
DOI: 10.1007/s10589-014-9700-x

## A posteriori error estimates of fully discrete finite-element schemes for nonlinear parabolic integro-differential optimal control problems

Zuliang Lu
Advances in Difference Equations 2014 (1) (2014)
DOI: 10.1186/1687-1847-2014-15

## An Error Analysis of Discontinuous Finite Element Methods for the Optimal Control Problems Governed by Stokes Equation

Asha K. Dond, Thirupathi Gudi and Ramesh C.H. Sau
Numerical Functional Analysis and Optimization 40 (4) 421 (2019)
DOI: 10.1080/01630563.2018.1538158

## A finite element method for elliptic optimal control problem on a non-convex polygon with corner singularities

Hyung Jun Choi, Woocheol Choi and Youngwoo Koh
Computers & Mathematics with Applications 75 (1) 45 (2018)
DOI: 10.1016/j.camwa.2017.08.029

## Approximation of an elliptic control problem by the finite element method

Donald A. French and J. Thomas King
Numerical Functional Analysis and Optimization 12 (3-4) 299 (1991)
DOI: 10.1080/01630569108816430

## Superconvergence of fully discrete rectangular mixed finite element methods of parabolic control problems

Tianliang Hou and Yanping Chen
Journal of Computational and Applied Mathematics 286 79 (2015)
DOI: 10.1016/j.cam.2014.11.052

## $L^\infty$-Estimates for Approximated Optimal Control Problems

C. Meyer and A. Rösch
SIAM Journal on Control and Optimization 44 (5) 1636 (2005)
DOI: 10.1137/040614621

## A posteriori error estimators for optimal distributed control governed by the first-order linear hyperbolic equation: DG method

Chunguang Xiong and Yuan Li
Numerical Methods for Partial Differential Equations 27 (3) 491 (2011)
DOI: 10.1002/num.20534

## Adaptive fully-discrete finite element methods for nonlinear quadratic parabolic boundary optimal control

Zuliang Lu
Boundary Value Problems 2013 (1) (2013)
DOI: 10.1186/1687-2770-2013-72

## Rough polyharmonic splines method for optimal control problem governed by parabolic systems with rough coefficient

Jiaoyan Zeng, Yanping Chen and Guichang Liu
Computers & Mathematics with Applications 80 (1) 121 (2020)
DOI: 10.1016/j.camwa.2020.03.001

## Subgrid scale eddy viscosity finite element method on optimal control of system governed by unsteady Oseen equations

Gang Chen and Minfu Feng
Computational Optimization and Applications 58 (3) 679 (2014)
DOI: 10.1007/s10589-014-9649-9

## Superconvergence for elliptic optimal control problems discretized by RT1 mixed finite elements and linear discontinuous elements

Tianliang Hou and Yanping Chen
Journal of Industrial & Management Optimization 9 (3) 631 (2013)
DOI: 10.3934/jimo.2013.9.631

## Optimal control of the Stokes equations: conforming and non-conforming finite element methods under reduced regularity

Serge Nicaise and Dieter Sirch
Computational Optimization and Applications 49 (3) 567 (2011)
DOI: 10.1007/s10589-009-9305-y

## ERROR ESTIMATES OF RT1 MIXED METHODS FOR DISTRIBUTED OPTIMAL CONTROL PROBLEMS

Tianliang Hou
Bulletin of the Korean Mathematical Society 51 (1) 139 (2014)
DOI: 10.4134/BKMS.2014.51.1.139

## Superconvergence of quadratic optimal control problems by triangular mixed finite element methods

Yanping Chen
International Journal for Numerical Methods in Engineering 75 (8) 881 (2008)
DOI: 10.1002/nme.2272
Thomas Apel, Johannes Pfefferer and Arnd Rösch
165 285 (2014)
DOI: 10.1007/978-3-319-05083-6_18

## Superconvergence Properties of Optimal Control Problems

C. Meyer and A. Rösch
SIAM Journal on Control and Optimization 43 (3) 970 (2004)
DOI: 10.1137/S0363012903431608

## Fourier Finite Volume Element Method for Two Classes of Optimal Control Problems Governed by Elliptic PDEs on Complex Connected Domain

Xiuxiu Lin, Mengya Su and Zhiyue Zhang
Numerical Functional Analysis and Optimization 41 (4) 379 (2020)
DOI: 10.1080/01630563.2019.1658602

## A GLOBAL SUPERCONVERGENT L∞-ERROR ESTIMATE OF MIXED FINITE ELEMENT METHODS FOR SEMILINEAR ELLIPTIC OPTIMAL CONTROL PROBLEMS

Li Li
Journal of Applied Analysis & Computation 5 (3) 313 (2015)
DOI: 10.11948/2015028

## Using piecewise linear functions in the numerical approximation of semilinear elliptic control problems

Eduardo Casas
Advances in Computational Mathematics 26 (1-3) 137 (2007)
DOI: 10.1007/s10444-004-4142-0

## A Priori Error Estimates for Optimal Control Problems Governed by Transient Advection-Diffusion Equations

Hongfei Fu and Hongxing Rui
Journal of Scientific Computing 38 (3) 290 (2009)
DOI: 10.1007/s10915-008-9224-6

## L 2-error estimates for Dirichlet and Neumann problems on anisotropic finite element meshes

Thomas Apel and Dieter Sirch
Applications of Mathematics 56 (2) 177 (2011)
DOI: 10.1007/s10492-011-0002-7

## On saturation effects in the Neumann boundary control of elliptic optimal control problems

Mariano Mateos and Arnd RÃ¶sch
PAMM 7 (1) 1060505 (2007)
DOI: 10.1002/pamm.200700674

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

Wenbin Liu, Heping Ma, Tao Tang and Ningning Yan
SIAM Journal on Numerical Analysis 42 (3) 1032 (2004)
DOI: 10.1137/S0036142902397090

## A priorianda posteriorierror estimates for the method of lumped masses for parabolic optimal control problems

Hongfei Fu and Hongxing Rui
International Journal of Computer Mathematics 88 (13) 2798 (2011)
DOI: 10.1080/00207160.2011.558575

## A Finite Element Method for Elliptic Dirichlet Boundary Control Problems

Michael Karkulik
Computational Methods in Applied Mathematics 20 (4) 827 (2020)
DOI: 10.1515/cmam-2019-0104
Gong Wei, Li Ruo, Yan Ningning and Zhao Weibo
585 (2008)
DOI: 10.1109/CHICC.2008.4605159

## Interpolation coefficients mixed finite element methods for general semilinear Dirichlet boundary elliptic optimal control problems

Zuliang Lu, Longzhou Cao and Lin Li
Applicable Analysis 97 (14) 2496 (2018)
DOI: 10.1080/00036811.2017.1376319

## Adaptive variational discretization approximation method for parabolic optimal control problems

Yuelong Tang and Yuchun Hua
Journal of Inequalities and Applications 2020 (1) (2020)
DOI: 10.1186/s13660-020-02506-6

## Adaptive finite element methods for the identification of distributed parameters in elliptic equation

Tao Feng, Ningning Yan and Wenbin Liu
Advances in Computational Mathematics 29 (1) 27 (2008)
DOI: 10.1007/s10444-007-9035-6

## Error estimates for the postprocessing approach applied to Neumann boundary control problems in polyhedral domains

Thomas Apel, Max Winkler and Johannes Pfefferer
IMA Journal of Numerical Analysis 38 (4) 1984 (2018)
DOI: 10.1093/imanum/drx059

## A priori error estimates for higher order variational discretization and mixed finite element methods of optimal control problems

Zuliang Lu, Yanping Chen and Yunqing Huang
Journal of Inequalities and Applications 2012 (1) (2012)
DOI: 10.1186/1029-242X-2012-95

## A priori error estimates for a linearized fracture control problem

Optimization and Engineering (2020)
DOI: 10.1007/s11081-020-09574-z

## On saturation effects in the Neumann boundary control of elliptic optimal control problems

Mariano Mateos and Arnd Rösch
Computational Optimization and Applications 49 (2) 359 (2011)
DOI: 10.1007/s10589-009-9299-5

## Adaptive Finite Elements for Elliptic Optimization Problems with Control Constraints

B. Vexler and W. Wollner
SIAM Journal on Control and Optimization 47 (1) 509 (2008)
DOI: 10.1137/070683416
Zuliang Lu and Xiao Huang
3519 (2012)
DOI: 10.1109/CCDC.2012.6244563

## A posteriori error estimates of mixed finite element methods for general optimal control problems governed by integro-differential equations

Zuliang Lu and Dayong Liu
Journal of Inequalities and Applications 2013 (1) (2013)
DOI: 10.1186/1029-242X-2013-351