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Volume 3, Issue 2
Superconvergence of Fully Discrete Finite Elements for Parabolic Control Problems with Integral Constraints

Y. Tang & Y. Hua

DOI: 10.4208/eajam.240313.280513a

East Asian J. Appl. Math., 3 (2013), pp. 138-153.

Published online: 2018-02

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  • Abstract

A quadratic optimal control problem governed by parabolic equations with integral constraints is considered. A fully discrete finite element scheme is constructed for the optimal control problem, with finite elements for the spatial but the backward Euler method for the time discretisation. Some superconvergence results of the control, the state and the adjoint state are proved. Some numerical examples are performed to confirm theoretical results.

  • Keywords

Superconvergence, finite element method, optimal control problems, parabolic equations, integral constraint.

  • AMS Subject Headings

35B37, 49J20, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-3-138, author = {Y. Tang and Y. Hua}, title = {Superconvergence of Fully Discrete Finite Elements for Parabolic Control Problems with Integral Constraints}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {3}, number = {2}, pages = {138--153}, abstract = {

A quadratic optimal control problem governed by parabolic equations with integral constraints is considered. A fully discrete finite element scheme is constructed for the optimal control problem, with finite elements for the spatial but the backward Euler method for the time discretisation. Some superconvergence results of the control, the state and the adjoint state are proved. Some numerical examples are performed to confirm theoretical results.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.240313.280513a}, url = {http://global-sci.org/intro/article_detail/eajam/10852.html} }
TY - JOUR T1 - Superconvergence of Fully Discrete Finite Elements for Parabolic Control Problems with Integral Constraints AU - Y. Tang & Y. Hua JO - East Asian Journal on Applied Mathematics VL - 2 SP - 138 EP - 153 PY - 2018 DA - 2018/02 SN - 3 DO - http://doi.org/10.4208/eajam.240313.280513a UR - https://global-sci.org/intro/article_detail/eajam/10852.html KW - Superconvergence, finite element method, optimal control problems, parabolic equations, integral constraint. AB -

A quadratic optimal control problem governed by parabolic equations with integral constraints is considered. A fully discrete finite element scheme is constructed for the optimal control problem, with finite elements for the spatial but the backward Euler method for the time discretisation. Some superconvergence results of the control, the state and the adjoint state are proved. Some numerical examples are performed to confirm theoretical results.

Y. Tang and Y. Hua. (2018). Superconvergence of Fully Discrete Finite Elements for Parabolic Control Problems with Integral Constraints. East Asian Journal on Applied Mathematics. 3 (2). 138-153. doi:10.4208/eajam.240313.280513a
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