Volume 31, Issue 1
A Posteriori Error Estimate of Finite Element Method for the Optimal Control with the Stationary Bénard Problem

Yanzhen Chang & Danping Yang

J. Comp. Math., 31 (2013), pp. 68-87.

Published online: 2013-02

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  • Abstract

In this paper, we consider the adaptive finite element approximation for the distributed optimal control associated with the stationary B\'{e}nard problem under the pointwise control constraint. The states and co-states are approximated by polynomial functions of lowest-order mixed finite element space or piecewise linear functions and control is approximated by piecewise constant functions. We give the a posteriori error estimates for the control, the states and co-states.

  • Keywords

Optimal control problem Stationary B\'{e}nard problem Nonlinear coupled system A posteriori error estimate

  • AMS Subject Headings

49J20 65N30.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-31-68, author = {Yanzhen Chang and Danping Yang}, title = {A Posteriori Error Estimate of Finite Element Method for the Optimal Control with the Stationary Bénard Problem}, journal = {Journal of Computational Mathematics}, year = {2013}, volume = {31}, number = {1}, pages = {68--87}, abstract = {

In this paper, we consider the adaptive finite element approximation for the distributed optimal control associated with the stationary B\'{e}nard problem under the pointwise control constraint. The states and co-states are approximated by polynomial functions of lowest-order mixed finite element space or piecewise linear functions and control is approximated by piecewise constant functions. We give the a posteriori error estimates for the control, the states and co-states.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1210-m3864}, url = {http://global-sci.org/intro/article_detail/jcm/9722.html} }
TY - JOUR T1 - A Posteriori Error Estimate of Finite Element Method for the Optimal Control with the Stationary Bénard Problem AU - Yanzhen Chang & Danping Yang JO - Journal of Computational Mathematics VL - 1 SP - 68 EP - 87 PY - 2013 DA - 2013/02 SN - 31 DO - http://doi.org/10.4208/jcm.1210-m3864 UR - https://global-sci.org/intro/article_detail/jcm/9722.html KW - Optimal control problem KW - Stationary B\'{e}nard problem KW - Nonlinear coupled system KW - A posteriori error estimate AB -

In this paper, we consider the adaptive finite element approximation for the distributed optimal control associated with the stationary B\'{e}nard problem under the pointwise control constraint. The states and co-states are approximated by polynomial functions of lowest-order mixed finite element space or piecewise linear functions and control is approximated by piecewise constant functions. We give the a posteriori error estimates for the control, the states and co-states.

Yanzhen Chang & Danping Yang. (1970). A Posteriori Error Estimate of Finite Element Method for the Optimal Control with the Stationary Bénard Problem. Journal of Computational Mathematics. 31 (1). 68-87. doi:10.4208/jcm.1210-m3864
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