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A FRAMEWORK FOR THE ERROR ANALYSIS OF DISCONTINUOUS FINITE ELEMENT METHODS FOR ELLIPTIC OPTIMAL CONTROL PROBLEMS AND APPLICATIONS TO C-0 IP METHODS

Chowdhury, Sudipto and Gudi, Thirupathi and Nandakumaran, AK (2015) A FRAMEWORK FOR THE ERROR ANALYSIS OF DISCONTINUOUS FINITE ELEMENT METHODS FOR ELLIPTIC OPTIMAL CONTROL PROBLEMS AND APPLICATIONS TO C-0 IP METHODS. In: NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 36 (11). pp. 1388-1419.

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Official URL: http://dx.doi.org/10.1080/01630563.2015.1068182

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.

Item Type: Journal Article
Additional Information: Copyright for this article belongs to the TAYLOR & FRANCIS INC, 530 WALNUT STREET, STE 850, PHILADELPHIA, PA 19106 USA
Keywords: Biharmonic; (CIP)-I-0 method; Discontinuous Galerkin; Error bounds; Finite element; Optimal control; Simply supported plate
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Depositing User: Id for Latest eprints
Date Deposited: 02 Dec 2015 08:27
Last Modified: 02 Dec 2015 08:27
URI: http://eprints.iisc.ac.in/id/eprint/52837

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