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Superconvergence of Rectangular Mixed Finite Element Methods for Constrained Optimal Control Problem

Superconvergence of Rectangular Mixed Finite Element Methods for Constrained Optimal Control Problem
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Year:    2010

Author:    Yanping Chen, Li Dai, Zuliang Lu

Advances in Applied Mathematics and Mechanics, Vol. 2 (2010), Iss. 1 : pp. 56–75

Abstract

We investigate the superconvergence properties of the constrained quadratic elliptic optimal control problem which is solved by using rectangular mixed finite element methods. We use the lowest order Raviart-Thomas mixed finite element spaces to approximate the state and co-state variables and use piecewise constant functions to approximate the control variable. We obtain the superconvergence of $\mathcal{O}(h^{1+s})$ $(0$<$s\leq$<$1)$ for the control variable. Finally, we present two numerical examples to confirm our superconvergence results.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.09-m0931

Advances in Applied Mathematics and Mechanics, Vol. 2 (2010), Iss. 1 : pp. 56–75

Published online:    2010-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    20

Keywords:    Constrained optimal control problem linear elliptic equation mixed finite element methods rectangular partition superconvergence properties.

Author Details

Yanping Chen

Li Dai

Zuliang Lu

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