Finite element approximation of elliptic Dirichlet optimal control problems

B. Vexler

doi:10.1080/01630560701493305

Finite element approximation of elliptic Dirichlet optimal control problems

B. Vexler

Johann Radon Institute for Computational and Applied Mathematics

Research output: Contribution to journal › Article › peer-review

35 Scopus citations

Abstract

We develop a priori error analysis for the finite element Galerkin discretization of elliptic Dirichlet optimal control problems. The state equation is given by an elliptic partial differential equation and the finite dimensional control variable enters the Dirichlet boundary conditions. We prove the optimal order of convergence and present a numerical example confirming our results.

Original language	English
Pages (from-to)	957-973
Number of pages	17
Journal	Numerical Functional Analysis and Optimization
Volume	28
Issue number	7-8
DOIs	https://doi.org/10.1080/01630560701493305
State	Published - Jul 2007
Externally published	Yes

Keywords

Dirichlet boundary control
Error estimates
Finite elements
Optimal control

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10.1080/01630560701493305

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abstract = "We develop a priori error analysis for the finite element Galerkin discretization of elliptic Dirichlet optimal control problems. The state equation is given by an elliptic partial differential equation and the finite dimensional control variable enters the Dirichlet boundary conditions. We prove the optimal order of convergence and present a numerical example confirming our results.",

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AB - We develop a priori error analysis for the finite element Galerkin discretization of elliptic Dirichlet optimal control problems. The state equation is given by an elliptic partial differential equation and the finite dimensional control variable enters the Dirichlet boundary conditions. We prove the optimal order of convergence and present a numerical example confirming our results.

KW - Dirichlet boundary control

KW - Error estimates

KW - Finite elements

KW - Optimal control

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JO - Numerical Functional Analysis and Optimization

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ER -

Finite element approximation of elliptic Dirichlet optimal control problems

Abstract

Keywords

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