Volume 3, Issue 4
Superconvergence of Parabolic Optimal Control Problems

Xiaoqing Xing & Yanping Chen

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 semidiscrete 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 = {Xiaoqing Xing and Yanping Chen}, title = {Superconvergence of Parabolic Optimal Control Problems}, 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 semidiscrete 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 Parabolic Optimal Control Problems AU - Xiaoqing Xing & Yanping Chen JO - Advances in Applied Mathematics and Mechanics VL - 4 SP - 401 EP - 419 PY - 2011 DA - 2011/03 SN - 3 DO - http://dor.org/10.4208/aamm.10-m1006 UR - https://global-sci.org/intro/aamm/176.html KW - Optimal control KW - mixed finite element KW - superconvergence KW - parabolic equations AB -

In this paper, we investigate the superconvergence results for optimal control problems governed by parabolic equations with semidiscrete 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.

Xiaoqing Xing & Yanping Chen. (1970). Superconvergence of Parabolic Optimal Control Problems. Advances in Applied Mathematics and Mechanics. 3 (4). 401-419. doi:10.4208/aamm.10-m1006
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