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Volume 5, Issue 4
Residual Based a Posteriori Error Estimates for Convex Optimal Control Problems Governed by Stokes-Darcy Equations

Ming Cui & Ningning Yan

DOI: 10.4208/nmtma.2012.m1113

Numer. Math. Theor. Meth. Appl., 5 (2012), pp. 602-634.

Published online: 2012-05

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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

Optimal control, Stokes-Darcy equations, a posteriori error estimate.

  • AMS Subject Headings

65N15, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-5-602, author = {Ming Cui and Ningning Yan}, title = {Residual Based a Posteriori Error Estimates for Convex Optimal Control Problems Governed by Stokes-Darcy Equations}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2012}, volume = {5}, number = {4}, pages = {602--634}, 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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2012.m1113}, url = {http://global-sci.org/intro/article_detail/nmtma/5952.html} }
TY - JOUR T1 - Residual Based a Posteriori Error Estimates for Convex Optimal Control Problems Governed by Stokes-Darcy Equations AU - Ming Cui & Ningning Yan JO - Numerical Mathematics: Theory, Methods and Applications VL - 4 SP - 602 EP - 634 PY - 2012 DA - 2012/05 SN - 5 DO - http://doi.org/10.4208/nmtma.2012.m1113 UR - https://global-sci.org/intro/article_detail/nmtma/5952.html KW - Optimal control, Stokes-Darcy equations, a posteriori error estimate. AB -

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.

Ming Cui and Ningning Yan. (2012). Residual Based a Posteriori Error Estimates for Convex Optimal Control Problems Governed by Stokes-Darcy Equations. Numerical Mathematics: Theory, Methods and Applications. 5 (4). 602-634. doi:10.4208/nmtma.2012.m1113
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