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Volume 4, Issue 4
A Posteriori Error Estimates of Mixed Methods for Quadratic Optimal Control Problems Governed by Parabolic Equations

Tianliang Hou, Yanping Chen & Yunqing Huang

DOI: 10.4208/nmtma.2011.m1017

Numer. Math. Theor. Meth. Appl., 4 (2011), pp. 439-458.

Published online: 2011-04

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  • Abstract

In this paper, we discuss the a posteriori error estimates of the mixed finite element method for quadratic optimal control problems governed by linear parabolic equations. The state and the co-state are discretized by the high order Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise constant functions. We derive a posteriori error estimates for both the state and the control approximation. Such estimates, which are apparently not available in the literature, are an important step towards developing reliable adaptive mixed finite element approximation schemes for the control problem.

  • Keywords

A posteriori error estimates, quadratic optimal control problems, parabolic equations, mixed finite element methods.

  • AMS Subject Headings

49J20, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-4-439, author = {Tianliang Hou, Yanping Chen and Yunqing Huang}, title = {A Posteriori Error Estimates of Mixed Methods for Quadratic Optimal Control Problems Governed by Parabolic Equations}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2011}, volume = {4}, number = {4}, pages = {439--458}, abstract = {

In this paper, we discuss the a posteriori error estimates of the mixed finite element method for quadratic optimal control problems governed by linear parabolic equations. The state and the co-state are discretized by the high order Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise constant functions. We derive a posteriori error estimates for both the state and the control approximation. Such estimates, which are apparently not available in the literature, are an important step towards developing reliable adaptive mixed finite element approximation schemes for the control problem.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2011.m1017}, url = {http://global-sci.org/intro/article_detail/nmtma/5977.html} }
TY - JOUR T1 - A Posteriori Error Estimates of Mixed Methods for Quadratic Optimal Control Problems Governed by Parabolic Equations AU - Tianliang Hou, Yanping Chen & Yunqing Huang JO - Numerical Mathematics: Theory, Methods and Applications VL - 4 SP - 439 EP - 458 PY - 2011 DA - 2011/04 SN - 4 DO - http://doi.org/10.4208/nmtma.2011.m1017 UR - https://global-sci.org/intro/article_detail/nmtma/5977.html KW - A posteriori error estimates, quadratic optimal control problems, parabolic equations, mixed finite element methods. AB -

In this paper, we discuss the a posteriori error estimates of the mixed finite element method for quadratic optimal control problems governed by linear parabolic equations. The state and the co-state are discretized by the high order Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise constant functions. We derive a posteriori error estimates for both the state and the control approximation. Such estimates, which are apparently not available in the literature, are an important step towards developing reliable adaptive mixed finite element approximation schemes for the control problem.

Tianliang Hou, Yanping Chen and Yunqing Huang. (2011). A Posteriori Error Estimates of Mixed Methods for Quadratic Optimal Control Problems Governed by Parabolic Equations. Numerical Mathematics: Theory, Methods and Applications. 4 (4). 439-458. doi:10.4208/nmtma.2011.m1017
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