On the Error Estimates for the Finite Element Approximation of a Class of Boundary Optimal Control Systems

被引：2

作者：

Gamallo, Pablo ^{[2
]}

Hernandez, Erwin ^{[1
]}

Peters, Andres ^{[3
]}

机构：

[1] Univ Tecn Federico Santa Maria, Dept Matemat, Valparaiso, Chile

[2] PERA Grp, Tecnol Avanzadas Inspiralia ITAV, Madrid, Spain

[3] Natl Univ Ireland, Hamilton Inst, Maynooth, Kildare, Ireland

来源：

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION | 2011年 / 32卷 / 04期

关键词：

Boundary optimal control problems; Error estimates; Finite element approximation; ELLIPTIC CONTROL-PROBLEMS; NUMERICAL APPROXIMATION; VARIATIONAL DISCRETIZATION; INEQUALITIES; CONVERGENCE;

D O I：

10.1080/01630563.2010.542359

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we consider an application of the abstract error estimate for a class of optimal control systems described by a linear partial differential equation (as stated in Numer. Funct. Anal. Optim. 2009; 30:523-547). The control is applied at the boundary and we consider both, Neumann and Dirichlet optimal control problems. Finite element methods are proposed to approximate the optimal control considering an approximation of the variational inequality resulting from the optimality conditions; this approach is known as classical one. We obtain optimal order error estimates for the control variable and numerical examples, taken from the literature, are included to illustrate the results.

引用

页码：383 / 396

页数：14

共 50 条

[11] A posteriori error estimates for mixed finite element approximation of nonlinear quadratic optimal control problems
Chen, Yanping
Lu, Zuliang
Fu, Min
[J]. OPTIMIZATION METHODS & SOFTWARE, 2013, 28 (01): : 37 - 53
[12] A posteriori error estimates of finite element methods for nonlinear quadratic boundary optimal control problem
Lu Z.
[J]. Numerical Analysis and Applications, 2011, 4 (3) : 210 - 222
[13] Error Estimates for Finite Element Approximation of Dirichlet Boundary Control for Stokes Equations in L2(Γ)
Zhou, Kaiye
Gong, Wei
[J]. JOURNAL OF SCIENTIFIC COMPUTING, 2022, 91 (02)
[14] OPTIMAL ERROR ESTIMATES FOR THE FINITE-ELEMENT SPECTRAL APPROXIMATION OF NONCOMPACT OPERATORS
MILLS, WH
[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 1979, 16 (04) : 704 - 718
[15] Error estimates and superconvergence of mixed finite element for quadratic optimal control
Chen, Yanping
Liu, Wenbin
[J]. INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING, 2006, 3 (03) : 311 - 321
[16] On Finite Element Error Estimates for Optimal Control Problems with Elliptic PDEs
Troeltzsch, Fredi
[J]. LARGE-SCALE SCIENTIFIC COMPUTING, 2010, 5910 : 40 - 53
[17] A PRIORI ERROR ESTIMATES FOR LEAST-SQUARES MIXED FINITE ELEMENT APPROXIMATION OF ELLIPTIC OPTIMAL CONTROL PROBLEMS
Fu, Hongfei
Rui, Hongxing
[J]. JOURNAL OF COMPUTATIONAL MATHEMATICS, 2015, 33 (02) : 113 - 127
[18] Error estimates for the finite-element approximation of a semilinear elliptic control problem
Casas, E
Tröltzsch, F
[J]. CONTROL AND CYBERNETICS, 2002, 31 (03): : 695 - 712
[19] Finite element error estimates for Neumann boundary control problems on graded meshes
Thomas Apel
Johannes Pfefferer
Arnd Rösch
[J]. Computational Optimization and Applications, 2012, 52 : 3 - 28
[20] Finite element error estimates for Neumann boundary control problems on graded meshes
Apel, Thomas
Pfefferer, Johannes
Roesch, Arnd
[J]. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, 2012, 52 (01) : 3 - 28

← 1 2 3 4 5 →