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Residual Based A Posteriori Error Estimates for Convex Optimal Control Problems Governed by Stokes-Darcy Equations

Published online by Cambridge University Press:  28 May 2015

Ming Cui  and
Ningning Yan
Ming Cui*
Affiliation:
Schools of Mathematics, Shandong University, Jinan 250100, China; LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China
Ningning Yan*
Affiliation:
LSEC, Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
*
Corresponding author.Email address:mingcui@sdu.edu.en
Corresponding author.Email address:ynn@amss.ac.en
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Abstract

In this paper, we derive a posteriori error estimates for finite element approximations of the optimal control problems governed by the Stokes-Darcy system. We obtain a posteriori error estimators for both the state and the control based on the residual of the finite element approximation. It is proved that the a posteriori error estimate provided in this paper is both reliable and efficient.

Keywords

65N1565N30Optimal controlStokes-Darcy equationsa posteriori error estimate
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 5 , Issue 4 , November 2012 , pp. 602 - 634
Copyright
Copyright © Global Science Press Limited 2012

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