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