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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

DOI: 10.4208/jcm.1210-m3864

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 Bénard 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 Bénard 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 Bénard 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, Stationary Bénard problem, Nonlinear coupled system, A posteriori error estimate. AB -

In this paper, we consider the adaptive finite element approximation for the distributed optimal control associated with the stationary Bénard 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 and Danping Yang. (2013). 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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