An interior penalty method for distributed optimal control problems governed by the biharmonic operator

Gudi, Thirupathi and Nataraj, Neela and Porwal, Kamana (2014) An interior penalty method for distributed optimal control problems governed by the biharmonic operator. In: COMPUTERS & MATHEMATICS WITH APPLICATIONS, 68 (12, B,). pp. 2205-2221.

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Abstract

In this paper, a C-0 interior penalty method has been proposed and analyzed for distributed optimal control problems governed by the biharmonic operator. The state and adjoint variables are discretized using continuous piecewise quadratic finite elements while the control variable is discretized using piecewise constant approximations. A priori and a posteriori error estimates are derived for the state, adjoint and control variables under minimal regularity assumptions. Numerical results justify the theoretical results obtained. The a posteriori error estimators are useful in adaptive finite element approximation and the numerical results indicate that the sharp error estimators work efficiently in guiding the mesh refinement. (C) 2014 Elsevier Ltd. All rights reserved.

Item Type:	Journal Article
Publication:	COMPUTERS & MATHEMATICS WITH APPLICATIONS
Publisher:	PERGAMON-ELSEVIER SCIENCE LTD
Additional Information:	Copy right for this article belongs to the PERGAMON-ELSEVIER SCIENCE LTD, THE BOULEVARD, LANGFORD LANE, KIDLINGTON, OXFORD OX5 1GB, ENGLAND
Keywords:	Distributed optimal control problems; Biharmonic operator; C-0 interior penalty method; a priori error estimate; a posteriori error estimate
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	24 Feb 2015 05:48
Last Modified:	24 Feb 2015 05:48
URI:	http://eprints.iisc.ac.in/id/eprint/50855

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