Volume 2, Issue 2
A Posteriori Error Estimates of Lowest Order Raviart-Thomas Mixed Finite Element Methods for Bilinear Optimal Control Problems

Zuliang Lu, Yanping Chen & Weishan Zheng

East Asian J. Appl. Math., 2 (2012), pp. 108-125.

Published online: 2018-02

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  • Abstract

A Raviart-Thomas mixed finite element discretization for general bilinear optimal control problems is discussed. The state and co-state are approximated by lowest order Raviart-Thomas mixed finite element spaces, and the control is discretized by piecewise constant functions. A posteriori error estimates are derived for both the coupled state and the control solutions, and the error estimators can be used to construct more efficient adaptive finite element approximations for bilinear optimal control problems. An adaptive algorithm to guide the mesh refinement is also provided. Finally, we present a numerical example to demonstrate our theoretical results.

  • Keywords

Bilinear optimal control problems lowest order Raviart-Thomas mixed finite element methods a posteriori error estimates adaptive algorithm

  • AMS Subject Headings

49J20 65N30

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COPYRIGHT: © Global Science Press

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@Article{EAJAM-2-108, author = {Zuliang Lu, Yanping Chen and Weishan Zheng}, title = {A Posteriori Error Estimates of Lowest Order Raviart-Thomas Mixed Finite Element Methods for Bilinear Optimal Control Problems}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {2}, number = {2}, pages = {108--125}, abstract = {

A Raviart-Thomas mixed finite element discretization for general bilinear optimal control problems is discussed. The state and co-state are approximated by lowest order Raviart-Thomas mixed finite element spaces, and the control is discretized by piecewise constant functions. A posteriori error estimates are derived for both the coupled state and the control solutions, and the error estimators can be used to construct more efficient adaptive finite element approximations for bilinear optimal control problems. An adaptive algorithm to guide the mesh refinement is also provided. Finally, we present a numerical example to demonstrate our theoretical results.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.080212.260312a}, url = {http://global-sci.org/intro/article_detail/eajam/10870.html} }
TY - JOUR T1 - A Posteriori Error Estimates of Lowest Order Raviart-Thomas Mixed Finite Element Methods for Bilinear Optimal Control Problems AU - Zuliang Lu, Yanping Chen & Weishan Zheng JO - East Asian Journal on Applied Mathematics VL - 2 SP - 108 EP - 125 PY - 2018 DA - 2018/02 SN - 2 DO - http://dor.org/10.4208/eajam.080212.260312a UR - https://global-sci.org/intro/article_detail/eajam/10870.html KW - Bilinear optimal control problems KW - lowest order Raviart-Thomas mixed finite element methods KW - a posteriori error estimates KW - adaptive algorithm AB -

A Raviart-Thomas mixed finite element discretization for general bilinear optimal control problems is discussed. The state and co-state are approximated by lowest order Raviart-Thomas mixed finite element spaces, and the control is discretized by piecewise constant functions. A posteriori error estimates are derived for both the coupled state and the control solutions, and the error estimators can be used to construct more efficient adaptive finite element approximations for bilinear optimal control problems. An adaptive algorithm to guide the mesh refinement is also provided. Finally, we present a numerical example to demonstrate our theoretical results.

Zuliang Lu, Yanping Chen & Weishan Zheng. (1970). A Posteriori Error Estimates of Lowest Order Raviart-Thomas Mixed Finite Element Methods for Bilinear Optimal Control Problems. East Asian Journal on Applied Mathematics. 2 (2). 108-125. doi:10.4208/eajam.080212.260312a
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