Volume 8, Issue 6
Error Estimates of Mixed Methods for Optimal Control Problems Governed by General Elliptic Equations

Adv. Appl. Math. Mech., 8 (2016), pp. 1050-1071.

Published online: 2018-05

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• Abstract

In this paper, we investigate the error estimates of mixed finite element methods for optimal control problems governed by general elliptic equations. 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 $H^{-1}$-error estimates both for the control variable and the state variables. Finally, a numerical example is given to demonstrate the theoretical results.

49J20, 65N30

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@Article{AAMM-8-1050, author = {Hou , Tianliang and Li , Li}, title = {Error Estimates of Mixed Methods for Optimal Control Problems Governed by General Elliptic Equations}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {8}, number = {6}, pages = {1050--1071}, abstract = {

In this paper, we investigate the error estimates of mixed finite element methods for optimal control problems governed by general elliptic equations. 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 $H^{-1}$-error estimates both for the control variable and the state variables. Finally, a numerical example is given to demonstrate the theoretical results.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2014.m807}, url = {http://global-sci.org/intro/article_detail/aamm/12131.html} }
TY - JOUR T1 - Error Estimates of Mixed Methods for Optimal Control Problems Governed by General Elliptic Equations AU - Hou , Tianliang AU - Li , Li JO - Advances in Applied Mathematics and Mechanics VL - 6 SP - 1050 EP - 1071 PY - 2018 DA - 2018/05 SN - 8 DO - http://doi.org/10.4208/aamm.2014.m807 UR - https://global-sci.org/intro/article_detail/aamm/12131.html KW - General elliptic equations, optimal control problems, superconvergence, error estimates, mixed finite element methods. AB -

In this paper, we investigate the error estimates of mixed finite element methods for optimal control problems governed by general elliptic equations. 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 $H^{-1}$-error estimates both for the control variable and the state variables. Finally, a numerical example is given to demonstrate the theoretical results.

Tianliang Hou & Li Li. (2020). Error Estimates of Mixed Methods for Optimal Control Problems Governed by General Elliptic Equations. Advances in Applied Mathematics and Mechanics. 8 (6). 1050-1071. doi:10.4208/aamm.2014.m807
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