Volume 2, Issue 1
Superconvergence of Rectangular Mixed Finite Element Methods for Constrained Optimal Control Problem

Adv. Appl. Math. Mech., 2 (2010), pp. 56-75.

Published online: 2010-02

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• 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.

• Keywords

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

49J20, 65N30

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• RIS
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@Article{AAMM-2-56, author = {Chen , Yanping and Dai , Li and Lu , Zuliang}, title = {Superconvergence of Rectangular Mixed Finite Element Methods for Constrained Optimal Control Problem}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2010}, volume = {2}, number = {1}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.09-m0931}, url = {http://global-sci.org/intro/article_detail/aamm/201.html} }
TY - JOUR T1 - Superconvergence of Rectangular Mixed Finite Element Methods for Constrained Optimal Control Problem AU - Chen , Yanping AU - Dai , Li AU - Lu , Zuliang JO - Advances in Applied Mathematics and Mechanics VL - 1 SP - 56 EP - 75 PY - 2010 DA - 2010/02 SN - 2 DO - http://doi.org/10.4208/aamm.09-m0931 UR - https://global-sci.org/intro/article_detail/aamm/201.html KW - Constrained optimal control problem, linear elliptic equation, mixed finite element methods, rectangular partition, superconvergence properties. AB -

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.

Yanping Chen, Li Dai & Zuliang Lu. (1970). Superconvergence of Rectangular Mixed Finite Element Methods for Constrained Optimal Control Problem. Advances in Applied Mathematics and Mechanics. 2 (1). 56-75. doi:10.4208/aamm.09-m0931
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