TY - JOUR

T1 - On the error estimates for the finite element approximation of a class of boundary optimal control systems

AU - Gamallo, Pablo

AU - Hernández, Erwin

AU - Peters, Andrés

N1 - Funding Information:
This work has been partially supported by Programa Basal CMM. U. de Chile. P. G. has been supported by Ministerio de Educación y Ciencia of Spain through grant 18-08-463B-750 and partially supported by Xunta de Galicia under project PGIDIT07PXIB105257PR. E. H. has been partially supported by Conicyt-Chile thought FONDECYT No. 1100490.

PY - 2011/4

Y1 - 2011/4

N2 - 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.

AB - 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.

KW - Boundary optimal control problems

KW - Error estimates

KW - Finite element approximation

UR - http://www.scopus.com/inward/record.url?scp=79952644903&partnerID=8YFLogxK

U2 - 10.1080/01630563.2010.542359

DO - 10.1080/01630563.2010.542359

M3 - Article

AN - SCOPUS:79952644903

VL - 32

SP - 383

EP - 396

JO - Numerical Functional Analysis and Optimization

JF - Numerical Functional Analysis and Optimization

SN - 0163-0563

IS - 4

ER -