A FrameWork for the Error Analysis of Discontinuous Finite Element Methods for Elliptic Optimal Control Problems and Applications to C 0 IP Methods

In this article, an abstract framework for the error analysis of discontinuous Galerkin methods for control constrained optimal control problems is developed. The analysis establishes the best approximation result from a priori analysis point of view and delivers a reliable and efficient a posterior...

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Published inNumerical functional analysis and optimization Vol. 36; no. 11; pp. 1388 - 1419
Main Authors Chowdhury, Sudipto, Gudi, Thirupathi, Nandakumaran, A. K.
Format Journal Article
LanguageEnglish
Published Taylor & Francis Group 02.11.2015
Subjects
Biharmonic
Discontinuous Galerkin
Error bounds
Finite element
IP method
Optimal control
Simply supported plate
Online AccessGet full text
ISSN0163-0563
1532-2467
DOI10.1080/01630563.2015.1068182

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Abstract In this article, an abstract framework for the error analysis of discontinuous Galerkin methods for control constrained optimal control problems is developed. The analysis establishes the best approximation result from a priori analysis point of view and delivers a reliable and efficient a posteriori error estimator. The results are applicable to a variety of problems just under the minimal regularity possessed by the well-posedness of the problem. Subsequently, the applications of C 0 interior penalty methods for a boundary control problem as well as a distributed control problem governed by the biharmonic equation subject to simply supported boundary conditions are discussed through the abstract analysis. Numerical experiments illustrate the theoretical findings.
AbstractList In this article, an abstract framework for the error analysis of discontinuous Galerkin methods for control constrained optimal control problems is developed. The analysis establishes the best approximation result from a priori analysis point of view and delivers a reliable and efficient a posteriori error estimator. The results are applicable to a variety of problems just under the minimal regularity possessed by the well-posedness of the problem. Subsequently, the applications of C 0 interior penalty methods for a boundary control problem as well as a distributed control problem governed by the biharmonic equation subject to simply supported boundary conditions are discussed through the abstract analysis. Numerical experiments illustrate the theoretical findings.
Author Chowdhury, Sudipto
Gudi, Thirupathi
Nandakumaran, A. K.
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  fullname: Nandakumaran, A. K.
  organization: Department of Mathematics , Indian Institute of Science
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SubjectTerms Biharmonic
Discontinuous Galerkin
Error bounds
Finite element
IP method
Optimal control
Simply supported plate
Title A FrameWork for the Error Analysis of Discontinuous Finite Element Methods for Elliptic Optimal Control Problems and Applications to C 0 IP Methods
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