Volume 6, Issue 5
A Priori Error Estimates of Finite Element Methods for Linear Parabolic Integro-Differential Optimal Control Problems

Wanfang Shen, Liang Ge, Danping Yang & Wenbin Liu

Adv. Appl. Math. Mech., 6 (2014), pp. 552-569.

Published online: 2014-06

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  • Abstract

In this paper, we study the mathematical formulation for an optimal control problem governed by a linear parabolic integro-differential equation and present the optimality conditions. We then set up its weak formulation and the finite element approximation scheme. Based on these we derive the a priori error estimates for its finite element approximation both in $H^1$ and $L^2$ norms. Furthermore some numerical tests are presented to verify the theoretical results.

  • Keywords

Optimal control linear parabolic integro-differential equations optimality conditions finite element methods a priori error estimate

  • AMS Subject Headings

65N30 65R20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-6-552, author = {Wanfang Shen, Liang Ge, Danping Yang and Wenbin Liu}, title = {A Priori Error Estimates of Finite Element Methods for Linear Parabolic Integro-Differential Optimal Control Problems}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2014}, volume = {6}, number = {5}, pages = {552--569}, abstract = {

In this paper, we study the mathematical formulation for an optimal control problem governed by a linear parabolic integro-differential equation and present the optimality conditions. We then set up its weak formulation and the finite element approximation scheme. Based on these we derive the a priori error estimates for its finite element approximation both in $H^1$ and $L^2$ norms. Furthermore some numerical tests are presented to verify the theoretical results.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2012.m30}, url = {http://global-sci.org/intro/article_detail/aamm/35.html} }
TY - JOUR T1 - A Priori Error Estimates of Finite Element Methods for Linear Parabolic Integro-Differential Optimal Control Problems AU - Wanfang Shen, Liang Ge, Danping Yang & Wenbin Liu JO - Advances in Applied Mathematics and Mechanics VL - 5 SP - 552 EP - 569 PY - 2014 DA - 2014/06 SN - 6 DO - http://dor.org/10.4208/aamm.2012.m30 UR - https://global-sci.org/intro/aamm/35.html KW - Optimal control KW - linear parabolic integro-differential equations KW - optimality conditions KW - finite element methods KW - a priori error estimate AB -

In this paper, we study the mathematical formulation for an optimal control problem governed by a linear parabolic integro-differential equation and present the optimality conditions. We then set up its weak formulation and the finite element approximation scheme. Based on these we derive the a priori error estimates for its finite element approximation both in $H^1$ and $L^2$ norms. Furthermore some numerical tests are presented to verify the theoretical results.

Wanfang Shen, Liang Ge, Danping Yang & Wenbin Liu. (1970). A Priori Error Estimates of Finite Element Methods for Linear Parabolic Integro-Differential Optimal Control Problems. Advances in Applied Mathematics and Mechanics. 6 (5). 552-569. doi:10.4208/aamm.2012.m30
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