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Volume 9, Issue 4
Mixed Finite Element Methods for Fourth Order Elliptic Optimal Control Problems

K. Manickam & P. Prakash

DOI: 10.4208/nmtma.2016.m1405

Numer. Math. Theor. Meth. Appl., 9 (2016), pp. 528-548.

Published online: 2016-09

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  • Abstract

In this paper, a priori error estimates are derived for the mixed finite element discretization of optimal control problems governed by fourth order elliptic partial differential equations. The state and co-state are discretized by Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise constant functions. The error estimates derived for the state variable as well as those for the control variable seem to be new. We illustrate with a numerical example to confirm our theoretical results.

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@Article{NMTMA-9-528, author = {}, title = {Mixed Finite Element Methods for Fourth Order Elliptic Optimal Control Problems}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2016}, volume = {9}, number = {4}, pages = {528--548}, abstract = {

In this paper, a priori error estimates are derived for the mixed finite element discretization of optimal control problems governed by fourth order elliptic partial differential equations. The state and co-state are discretized by Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise constant functions. The error estimates derived for the state variable as well as those for the control variable seem to be new. We illustrate with a numerical example to confirm our theoretical results.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2016.m1405}, url = {http://global-sci.org/intro/article_detail/nmtma/12388.html} }
TY - JOUR T1 - Mixed Finite Element Methods for Fourth Order Elliptic Optimal Control Problems JO - Numerical Mathematics: Theory, Methods and Applications VL - 4 SP - 528 EP - 548 PY - 2016 DA - 2016/09 SN - 9 DO - http://doi.org/10.4208/nmtma.2016.m1405 UR - https://global-sci.org/intro/article_detail/nmtma/12388.html KW - AB -

In this paper, a priori error estimates are derived for the mixed finite element discretization of optimal control problems governed by fourth order elliptic partial differential equations. The state and co-state are discretized by Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise constant functions. The error estimates derived for the state variable as well as those for the control variable seem to be new. We illustrate with a numerical example to confirm our theoretical results.

K. Manickam & P. Prakash. (2020). Mixed Finite Element Methods for Fourth Order Elliptic Optimal Control Problems. Numerical Mathematics: Theory, Methods and Applications. 9 (4). 528-548. doi:10.4208/nmtma.2016.m1405
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