Volume 4, Issue 6
Error Estimates and Superconvergence of Mixed Finite Element Methods for Optimal Control Problems with Low Regularity

Yanping Chen, Tianliang Hou & Weishan Zheng

Adv. Appl. Math. Mech., 4 (2012), pp. 751-768.

Published online: 2012-12

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  • Abstract

In this paper, we investigate the error estimates and superconvergence property of mixed finite element methods for elliptic optimal control problems. The state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise constant functions. We derive L^2 and L^\infty-error estimates for the control variable. Moreover, using a recovery operator, we also derive some superconvergence results for the control variable. Finally, a numerical example is given to demonstrate the theoretical results.

  • Keywords

Elliptic equations optimal control problems superconvergence error estimates mixed finite element methods

  • AMS Subject Headings

49J20 65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-4-751, author = {Yanping Chen, Tianliang Hou and Weishan Zheng}, title = {Error Estimates and Superconvergence of Mixed Finite Element Methods for Optimal Control Problems with Low Regularity}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2012}, volume = {4}, number = {6}, pages = {751--768}, abstract = {

In this paper, we investigate the error estimates and superconvergence property of mixed finite element methods for elliptic optimal control problems. The state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise constant functions. We derive L^2 and L^\infty-error estimates for the control variable. Moreover, using a recovery operator, we also derive some superconvergence results for the control variable. Finally, a numerical example is given to demonstrate the theoretical results.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.12-12S05}, url = {http://global-sci.org/intro/article_detail/aamm/147.html} }
TY - JOUR T1 - Error Estimates and Superconvergence of Mixed Finite Element Methods for Optimal Control Problems with Low Regularity AU - Yanping Chen, Tianliang Hou & Weishan Zheng JO - Advances in Applied Mathematics and Mechanics VL - 6 SP - 751 EP - 768 PY - 2012 DA - 2012/12 SN - 4 DO - http://doi.org/10.4208/aamm.12-12S05 UR - https://global-sci.org/intro/article_detail/aamm/147.html KW - Elliptic equations KW - optimal control problems KW - superconvergence KW - error estimates KW - mixed finite element methods AB -

In this paper, we investigate the error estimates and superconvergence property of mixed finite element methods for elliptic optimal control problems. The state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise constant functions. We derive L^2 and L^\infty-error estimates for the control variable. Moreover, using a recovery operator, we also derive some superconvergence results for the control variable. Finally, a numerical example is given to demonstrate the theoretical results.

Yanping Chen, Tianliang Hou & Weishan Zheng. (1970). Error Estimates and Superconvergence of Mixed Finite Element Methods for Optimal Control Problems with Low Regularity. Advances in Applied Mathematics and Mechanics. 4 (6). 751-768. doi:10.4208/aamm.12-12S05
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