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Mixed Finite Element Methods for Fourth Order Elliptic Optimal Control Problems

Part of: Partial differential equations, boundary value problems

Published online by Cambridge University Press:  17 November 2016

K. Manickam  and
P. Prakash
K. Manickam*
Affiliation:
Department of Mathematics, Periyar University, Salem 636 011, India
P. Prakash*
Affiliation:
Department of Mathematics, Periyar University, Salem 636 011, India
*
*Corresponding author. Email addresses:pprakashmaths@gmail.com (P. Prakash), kkmmanickam@gmail.com (K. Manickam)
*Corresponding author. Email addresses:pprakashmaths@gmail.com (P. Prakash), kkmmanickam@gmail.com (K. Manickam)

Abstract

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In this paper, a priori error estimates are derived for the mixed finite element discretization of optimal control problems governed by fourth order elliptic partial differential equations. The state and co-state are discretized by Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise constant functions. The error estimates derived for the state variable as well as those for the control variable seem to be new. We illustrate with a numerical example to confirm our theoretical results.

Keywords

fourth order mixed finite element methodsoptimal control problemsL 2 projectiona priori error estimates

MSC classification

Secondary: 65N15: Error bounds 65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods

Information

Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 9 , Issue 4 , November 2016 , pp. 528 - 548
Copyright
Copyright © Global-Science Press 2016 

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