### A POSTERIORI ERROR ESTIMATE OF FINITE ELEMENT METHOD FOR THE OPTIMAL CONTROL WITH THE STATIONARY BÉNARD PROBLEM

Yanzhen Chang1, Danping Yang2

1. 1. Department of Mathematics, Beijing University of Chemical Technology, Beijing 100029, China;
2. Department of Mathematics, East China Normal University, Shanghai 200062, China
• Received:2011-09-09 Revised:2012-10-25 Online:2013-01-15 Published:2013-01-17
• Supported by:

This paper is supported in part by China NSF under the grant 11101025, the Fundamental Research Funds for the Central Universities and the Science and Technology Development Planning Project of Shandong Province under the grant 2011GGH20118.

Yanzhen Chang, Danping Yang. A POSTERIORI ERROR ESTIMATE OF FINITE ELEMENT METHOD FOR THE OPTIMAL CONTROL WITH THE STATIONARY BÉNARD PROBLEM[J]. Journal of Computational Mathematics, 2013, 31(1): 68-87.

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 lowestorder 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.

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