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Volume 3, Issue 4
Superconvergence of Mixed Methods for Optimal Control Problems Governed by Parabolic Equations

Xiaoqing Xing & Yanping Chen

DOI: 10.4208/aamm.10-m1006

Adv. Appl. Math. Mech., 3 (2011), pp. 401-419.

Published online: 2011-03

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  • Abstract

In this paper, we investigate the superconvergence results for optimal control problems governed by parabolic equations with semi-discrete mixed finite element approximation. We use the lowest order mixed finite element spaces to discrete the state and costate variables while use piecewise constant function to discrete the control variable. Superconvergence estimates for both the state variable and its gradient variable are obtained.

  • Keywords

Optimal control, mixed finite element, superconvergence, parabolic equations.

  • AMS Subject Headings

65L10, 65L12

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-3-401, author = {Xing , Xiaoqing and Chen , Yanping}, title = {Superconvergence of Mixed Methods for Optimal Control Problems Governed by Parabolic Equations}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2011}, volume = {3}, number = {4}, pages = {401--419}, abstract = {

In this paper, we investigate the superconvergence results for optimal control problems governed by parabolic equations with semi-discrete mixed finite element approximation. We use the lowest order mixed finite element spaces to discrete the state and costate variables while use piecewise constant function to discrete the control variable. Superconvergence estimates for both the state variable and its gradient variable are obtained.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.10-m1006}, url = {http://global-sci.org/intro/article_detail/aamm/176.html} }
TY - JOUR T1 - Superconvergence of Mixed Methods for Optimal Control Problems Governed by Parabolic Equations AU - Xing , Xiaoqing AU - Chen , Yanping JO - Advances in Applied Mathematics and Mechanics VL - 4 SP - 401 EP - 419 PY - 2011 DA - 2011/03 SN - 3 DO - http://doi.org/10.4208/aamm.10-m1006 UR - https://global-sci.org/intro/article_detail/aamm/176.html KW - Optimal control, mixed finite element, superconvergence, parabolic equations. AB -

In this paper, we investigate the superconvergence results for optimal control problems governed by parabolic equations with semi-discrete mixed finite element approximation. We use the lowest order mixed finite element spaces to discrete the state and costate variables while use piecewise constant function to discrete the control variable. Superconvergence estimates for both the state variable and its gradient variable are obtained.

Xing , Xiaoqing and Chen , Yanping. (2011). Superconvergence of Mixed Methods for Optimal Control Problems Governed by Parabolic Equations. Advances in Applied Mathematics and Mechanics. 3 (4). 401-419. doi:10.4208/aamm.10-m1006
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